Nonlinear Analysis and Boundary Value Problems

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Analysis".

Deadline for manuscript submissions: 28 February 2027 | Viewed by 1285

Special Issue Editor


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Guest Editor
School of Science, Jiangnan University, Wuxi 214122, China
Interests: variational methods; partial differential equations
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Special Issue Information

Dear Colleagues,

The methods of nonlinear functional analysis include the topological degrees of finite and infinite dimensions, critical point theory, Morse theory, etc., which produce fruitful results related to existence and multiplicity, as well as solutions to various differential equations arising from the mathematical modelling of natural phenomena.

The primary goal of this Special Issue, entitled “Nonlinear Analysis and Boundary Value Problems”, is to provide a platform for researchers and academicians to report on new initiatives and developments in this field. Original research as well as review articles are encouraged.

Potential topics include, but are not limited to, the following:

  • Topological nonlinear analysis and applications;
  • Fixed-point problems;
  • Critical point theory and its applications;
  • Morse theory and its applications;
  • Bifurcation theory;
  • Variational methods and PDEs;
  • Nonlinear elliptic equations;
  • Nonlocal nonlinear PDEs;
  • Boundary value problems in Ordinary Differential Equations;
  • Asymptotic behavior in nonlinear elliptic problems.

Prof. Dr. Yang Yang
Guest Editor

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Keywords

  • variational method
  • critical point theory
  • Morse theory
  • boundary value problems
  • partial differential equations
  • ordinary differential equation

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Published Papers (2 papers)

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Research

15 pages, 274 KB  
Article
Normalized Solution for the Fractional Kirchhoff System with Hardy Nonlinearities
by Yufei Wang and Yang Yang
Axioms 2026, 15(5), 369; https://doi.org/10.3390/axioms15050369 - 15 May 2026
Viewed by 115
Abstract
In this paper, we consider the existence of normalized solutions for the fractional Kirchhoff system with Hardy critical nonlinearities. The problem combines the challenges of nonlocal operators, singular critical effects, and a variational framework with fixed mass conditions. By employing the minimax theorem, [...] Read more.
In this paper, we consider the existence of normalized solutions for the fractional Kirchhoff system with Hardy critical nonlinearities. The problem combines the challenges of nonlocal operators, singular critical effects, and a variational framework with fixed mass conditions. By employing the minimax theorem, analyzing the Palais–Smale sequence and restricting to radial functions, we overcome the loss of strong convergence at critical energy levels. Under L2-supercritical case, we prove the existence of positive radial normalized solutions, along with the positivity of the corresponding Lagrange multipliers. Full article
(This article belongs to the Special Issue Nonlinear Analysis and Boundary Value Problems)
28 pages, 1053 KB  
Article
Optimal Boundary-Flux Control of a Sharp Moving Interface in the Classical Two-Phase Stefan Problem
by Khalid Ali Alanezy and Jihad Souissi
Axioms 2025, 14(11), 840; https://doi.org/10.3390/axioms14110840 - 17 Nov 2025
Viewed by 836
Abstract
In this paper, we study the optimal boundary control of solidification governed by the classical two-phase Stefan problem with a sharp moving interface. The main objective is to formulate an optimal control problem for interface motion using boundary heat-flux control. The control acts [...] Read more.
In this paper, we study the optimal boundary control of solidification governed by the classical two-phase Stefan problem with a sharp moving interface. The main objective is to formulate an optimal control problem for interface motion using boundary heat-flux control. The control acts as a Neumann heat flux on a designated boundary segment and steers the interface through the Stefan condition. Using an enthalpy formulation, we prove well-posedness under boundary control and establish Lipschitz continuity of the control-to-state map and continuous dependence on the initial data. We then derive first-order necessary optimality conditions using a Lagrangian approach and propose a practical algorithm that couples a semismooth Newton method with Sequential Quadratic Programming (SQP) to compute the optimal boundary flux. Full article
(This article belongs to the Special Issue Nonlinear Analysis and Boundary Value Problems)
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