This paper is concerned with the existence result of a sequence of infinitely many small energy solutions to the fractional r(·)-Laplacian equations of Kirchhoff–Schrödinger type with concave–convex nonlinearities when the con...
By developing the direct method of moving planes, we study the radial symmetry of nonnegative solutions for a fractional Laplacian system with different negative powers: (−Δ)α2u(x)+u−γ(x)+v−q(x)=0,x∈RN, (...
In this article, we consider the following fractional (p,q)-Laplacian problem (−Δ)ps1u+(−Δ)qs2u+V(x)(|u|p−2u+|u|q−2u)=f(u)+λ|u|r−2u, where x∈RN, (−Δ)ps1 is the fractional p-Laplacian o...
By using the Ekeland variational principle and Nehari manifold, we study the following fractional p-Laplacian Kirchhoff equations: M[u]s,pp+∫RNV(x)|u|pdx[(−Δ)psu+V(x)|u|p−2u]=λ|u|q−2uln|u|,x∈RN,(P). In these eq...
We are concerned with the existence and multiplicity of normalized solutions to the fractional Schrödinger equation (−Δ)su+V(εx)u=λu+h(εx)f(u)inRN,∫RN|u|2dx=a,, where (−Δ)s is the fractional Lap...
In this paper, we will study a singular problem involving the fractional (q1(x,.)-q2(x,.))-Laplacian operator in the whole space RN,(N≥2). More precisely, we combine the variational method with monotonicity arguments to prove that the associated f...
We study the existence and multiplicity of normalized solutions to the fractional logarithmic Schrödinger equation (−Δ)su+V(ϵx)u=λu+ulogu2inRN, under the mass constraint ∫RN|u|2dx=a. Here, N≥2, a,ϵ>0, &la...
In this paper, we consider the following class of the fractional p&q-Laplacian problem: (−Δ)psu+(−Δ)qsu+V(x)(|u|p−2u+|u|q−2u)+g(x)|u|r−2u=K(x)f(x,u)+h(u),x∈RN,V:RN→R+ is a potential function, an...
In this paper, we study the following non-local problem in fractional Orlicz–Sobolev spaces: (−ΔΦ)su+V(x)a(|u|)u=f(x,u), x∈RN, where (−ΔΦ)s(s∈(0,1)) denotes the non-local and maybe non-homogeneous...
In this paper, we studied a class of semilinear pseudo-parabolic equations of the Kirchhoff type involving the fractional Laplacian with logarithmic nonlinearity: ut+M([u]s2)(−Δ)su+(−Δ)sut=|u|p−2uln|u|,in Ω&ti...
We are concerned with the following elliptic equations: (−Δ)psv+V(x)|v|p−2v=λa(x)|v|r−2v+g(x,v)inRN, where (−Δ)ps is the fractional p-Laplacian operator with 0<s<1<r<p<+∞, sp<N, the p...
We herein discuss the following elliptic equations: M ∫ R N ∫ R N | u ( x ) − u ( y ) | p | x − y | N + p s d x d y ( − Δ ) p s u + V ( x ) | u | p − 2 u = λ f (...