610 Results Found

In this article, we investigate a class of fractional Choquard equation with critical Sobolev exponent. By exploiting a monotonicity technique and global compactness lemma, the existence of ground state solutions for this equation is obtained. In add...

In this article, we investigate the existence of a nontrivial solution for the nonlinear Choquard equation with upper critical exponent see Equation (6). The Riesz potential in this case has never been studied. We establish the existence of the groun...

In this paper, we study a class of nonlinear Choquard equation driven by the fractional Laplacian. When the potential function vanishes at infinity, we obtain the existence of a ground state solution for the fractional Choquard equation by using a no...

We investigate a class of fractional linearly coupled Choquard systems. For the subcritical case and all critical cases, we prove the existence, nonexistence and symmetry of positive ground state solutions of systems, by using the Nehari manifold met...

In this paper, we consider a new kind of Kirchhoff-type equation which is stated in the introduction. Under certain assumptions on potentials, we prove by variational methods that the equation has at least a ground state solution and investigate the...

We study the following quasilinear Schrödinger equation involving critical exponent $-\Delta u+V\left(x\right)u-\Delta \left(u^2\right)u=A\left(x\right){|u|}^{p-1}u+\lambda B\left(x\right)u^{\frac{3N+2}{N-2}}$ , ...

We take a look at the fractional Kirchhoff problem in this paper. Using a variational approach, we show that there exists a ground state solution for this problem. Furthermore, using the approach developed by Szulkin and Weth, we also find that posit...

We present the construction of the ground state of the Gross–Pitaevskii–Poisson equations using genetic algorithms. By employing numerical solutions, we develop an empirical formula for the density that works within the considered paramet...

In this paper, we study the following non-local problem in fractional Orlicz–Sobolev spaces: ${(-{\Delta }_{\Phi })}^{s}u+V\left(x\right)a(|u|)u=f(x,u), x\in {\mathbb{R}}^N$, where ${(-{\Delta }_{\Phi })}^s(s\in (0,1))$ denotes the non-local and maybe non-homogeneous...

We prove the existence of a positive ground state solution for a fractional $(p,q)$-Laplacian Choquard equation that features both a singularity and an upper critical exponent. The proof relies on a combination of the Nehari manifold technique and Ekel...

The purpose of this paper is to investigate the existence and asymptotic properties of solutions to a Kirchhoff-type equation with Hardy potential and Berestycki–Lions conditions. Firstly, we show that the equation has a positive radial ground-...

In this article, we consider the singular $p$-biharmonic problem involving Hardy potential and critical Hardy–Sobolev exponent. Firstly, we study the existence of ground state solutions by using the minimization method on the associated Nehari ma...

In this paper, we study a class of nonlocal Schrödinger–Poisson–Slater equations: $-\Delta u+u+\lambda \left(I_{\alpha }\ast {\left|u\right|}^q\right){\left|u\right|}^{q-2}u={\left|u\right|}^{p-2}u$, where $q,p>1$, $\lambda >0$, and $I_{\alpha }$ is the Riesz potential. We obtai...

In this article, we are interested in the study of the following Kirchhoff–Choquard equations: $-\left(a+b{\int }_{{\mathbb{R}}^2}{|\nabla u|}^2\mathrm{d}x\right)\Delta u+V\left(x\right)u=\lambda (ln|x|\ast u^2)u+f\left(u\right),x\in {\mathbb{R}}^2,$ where $\lambda >0,a>0,b>0$, V and f are continuous fun...

We consider quasi-one-dimensional (Q1D) continuous waves (CWs) in the two-dimensional (2D) optical system with the cubic–quintic (CQ) nonlinearity and a Q1D potential trough. In the case of a smooth trough profile, we confirm the known modulati...

This paper is devoted to the study of the following fractional Choquard equation with prescribed $L^2$ norm: $\left\{\begin{array}{c}{(-\mathrm{\Delta })}^{s}u+\mu u=\left(I_{\alpha }\ast F\left(u\right)\right)F^{\prime }\left(u\right)\mathrm{in}{\mathbb{R}}^N,\hfill \\ {\parallel u\parallel }_{L^2\left({\mathbb{R}}^N\right)}=a,\hfill \end{array}\right.$ where $N\ge 2$, $s\in (0,1)$, $I_{\alpha }$ is the Riesz potentia...

In this paper, we study the existence/non-existence of ground states for the following type of elliptic equations with mixed local and nonlocal operators and general nonlinearity: ${(-▵)}^{s}u-▵u+\lambda u=f\left(u\right),x\in {\mathbb{R}}^N$, which...

Accurate prediction of the temperature field around shallow-buried freezing pipes is important for the design and assessment of artificial ground freezing systems in shallow tunnel and underground structure construction. This study develops a semi-an...

In this paper we discuss some results on the existence of solutions for an elliptic system appearing in physical sciences. In particular the system appears when we look at standing wave solutions in the electrostatic situation for the Schrödinge...

We investigate ground states of a (nonlocal) nonlinear Schrödinger equation which generalizes classical (fractional, relativistic, etc.) Schrödinger equations, so that we extend relevant results and study common properties of these equation...

It is experimentally established that there is no ground triplet state of the natural $He$ atom. There is also no exact analytical solution to the Schrödinger equation corresponding to this state. For a two-dimensional two-electron ‘artifici...

In one of our previous papers, it was shown that for the ground state of hydrogenic atoms/ions, it is possible to match the interior (inside the nucleus) solution of the Dirac equation with the singular exterior solution of the Dirac equation, so tha...

This paper studies the existence, regularity, and properties of normalized ground state solutions for the mixed fractional Schrödinger equations. For subcritical cases, we establish the boundedness and Sobolev regularity of solutions, derive Poh...

A Bose-Fermi mixture, consisting of both bosons and fermions, exhibits distinctive quantum coherence and phase transitions, offering valuable insights into many-body quantum systems. The ground state, as the system’s lowest energy configuration...

In this paper, characteristic ultraviolet absorption spectra are presented for benzene and chlorobenzene in transparent hexagonal water–ice solutions at temperatures between 273 K and 78 K. In addition, the liquid solution spectra at 292 K have...

In this paper, we study the existence and asymptotic behaviors of ground state solutions to a fourth-order nonlinear Schrödinger equation with mass-critical exponent, where the fourth-order term appears as a perturbation with $\epsilon >0$. By...

Grounding fault analysis is of vital importance for low voltage direct current (LVDC) supply and utilization systems. However, the existing DC grounding fault model is inappropriate for LVDC supply and utilization system. In order to provide an appro...

Organic luminescent materials with high luminescence efficiency in both solution and solid states, namely dual-state emission (DSE), have attracted considerable attention due to their promising applications in various fields. In order to enrich the v...

6-Thioguanine, an immunosuppressant and anticancer prodrug, has been shown to induce DNA damage and cell death following exposure to UVA radiation. Its metabolite, 6-thioguanosine, plays a major role in the prodrug’s overall photoreactivity. However,...

In this paper, we consider a logarithmic fractional Schrödinger-Poisson system where the potential is a sign-changing function. When the potential is coercive, we get the existence of infinitely many solutions for the system. When the potential...

In this work, we investigate the ground state properties and collective excitations of a dipolar Bose–Einstein condensate that self-binds into a quantum droplet, stabilized by quantum fluctuations. We demonstrate that a sum rule approach can ac...

Variational perturbation theory was used to solve the Schrödinger equation for a hydrogen atom confined at the center of an impenetrable cavity. Ground state and excited state energies and expectation values calculated from the perturbation wavefunct...

In this research study, we derive the exact solutions of the Bloch equations describing the dynamics of a two-level atom with dephasing. In the two-level atom, a strong laser pump couples a ground state to an upper excited state with a time-dependent...

The novel complex [Fe^III(HL)(L)]·2dmf (1) was successfully synthesized by reacting iron chloride with dimethylformamide solution of the Schiff base ligand (H₂L). The ligand was prepared in situ through the condensation of 5-bromo-salicylaldehy...

The photophysical processes and photochemical reactions of 1,4-di(azastyryl)benzene (1) derivative {[(E,E)-1](ClO₄)₂} were investigated by absorption, luminescence, and laser kinetic spectroscopy in the water solution. The observed photo processes in...

We prove the existence of a spherically symmetric solution for a Schrödinger equation with a nonlocal nonlinearity of Choquard type. This term is assumed to be subcritical and satisfy almost optimal assumptions. The mass of of the solution, described...

Intramolecular charge transfer (ICT) of curcumin in dimethyl sulfoxide (DMSO) solution in the excited state was investigated by femtosecond electronic and vibrational spectroscopy. Excited-state Raman spectra of curcumin in the locally-excited and ch...

Artificial ground freezing is widely used for shaft sinking in deep water-rich alluvium, but conventional frozen-wall design often treats the wall as an isolated thick cylinder loaded by the full horizontal ground pressure. This paper develops an ana...

There is compelling evidence that the absorption of low-energy UV radiation directly by DNA in solution generates guanine radicals with quantum yields that are strongly dependent on the secondary structure. Key players in this unexpected phenomenon a...

This paper focuses on the symmetry and monotonicity of non-negative solutions to a mixed local and nonlocal weighted elliptic problem. This problem generalizes the ground-state representation of elliptic equations with the Hardy potential. The novelt...

State-of-the-art commercial simulators (e.g., Eclipse, CMG) predominantly employ finite difference schemes, which face persistent challenges in modeling strongly nonlinear seepage dynamics. This study explores the application of the Ritz method, grou...

Ground surface roughness is difficult to predict through a physical model due to its complex influencing factors. BP neural networks (BPNNs), a promising method, have been widely applied in the prediction of surface roughness. This paper uses the con...

Quantum Heisenberg chain and square lattices are important paradigms of a low-dimensional magnetism. Their ground states are determined by the strength of quantum fluctuations. Correspondingly, the ground state of a rectangular lattice interpolates b...

A novel series of the title compound 4-(5-arylazo-2-hydroxystyryl)-1-methylpyridinium iodide 6 has been synthesized via condensation reactions of the arylazosalicylaldehyde derivatives 4a–i with 1-methyl-picolinium iodide 5. The structures of the new...

In this paper, we delve into the following nonlinear fractional Kirchhoff-type problem ${(a+b||(-\Delta )}^{{\displaystyle \frac{s}{2}}}{u\left|\right|}_2^2{)(-\Delta )}^{s}u+\lambda u=g\left(u\right)+{\left|u\right|}^{2_s^{*}-2}u$ in ${\mathbb{R}}^3$ with prescribed mass ${\int }_{{\mathbb{R}}^3}{\left|u\right|}^{2}dx=\rho >0,$ where $s\in ({\displaystyle \frac{3}{4}},1),\lambda \&i$...

The synthesis and characterization of two new complexes, namely Pt(1,3-bis(4-(4-hexyl-2-thienyl)-pyridin-2-yl)-5-mesitylbenzene)Cl and Pt(1,3-bis(4-(4-hexyl-2-thienyl)-pyridin-2-yl)-5-(2-thienyl)benzene)Cl, are reported. Both exhibit luminescence qua...

The method of quantum dynamics is employed to investigate the mean strategy in the swarm intelligence algorithm. The physical significance of the population mean point is explained as the location where the optimal solution with the highest likelihoo...

We consider a hybrid nanostructure composed by semiconductor quantum dot coupled to a metallic nanoparticle and investigate the efficient creation of biexciton state in the quantum dot, when starting from the ground state and using linearly polarized...

The paper discusses the state-of-the-art of locomotion systems for ground mobile robots comprising tracks. Tracked locomotion, due to the large contact surface with the ground, is particularly suitable for tackling soft, yielding, and irregular terra...

Dioxazolones are important precursors for generating nitrenes (highly reactive intermediates widely used for carbon–nitrogen bond formation in organic synthesis) upon exposure to light or heat. The photochemical reaction dynamics of 3-phenyl-1,...