Results 31 to 40 of about 76 (76)

Concentration–Compactness Principle to a Weighted Moser–Trudinger Inequality and Its Application

Journal of Mathematics, Volume 2025, Issue 1, 2025.
We employ level‐set analysis of functions to establish a sharp concentration–compactness principle for the Moser–Trudinger inequality with power weights in R+2. Furthermore, we systematically prove the existence of ground state solutions to the associated nonlinear partial differential equation.
Yubo Ni, Agacik Zafer
wiley   +1 more source

Least energy solutions for a class of (p1,p2)$(p_{1}, p_{2})$‐Kirchhoff‐type problems in RN$\mathbb {R}^{N}$ with general nonlinearities

Journal of the London Mathematical Society, Volume 110, Issue 4, October 2024.
Abstract We examine the following (p1,p2)$(p_{1}, p_{2})$‐Kirchhoff‐type problem: −M1∥∇u∥Lp1(RN)p1Δp1u−M2∥∇u∥Lp2(RN)p2Δp2u=g(u)inRN,u∈W1,p1(RN)∩W1,p2(RN),$$\begin{equation*} {\left\lbrace \def\eqcellsep{&}\begin{array}{ll}-M_{1}\left(\Vert \nabla u\Vert ^{p_{1}}_{L^{p_{1}}(\mathbb {R}^{N})}\right)\Delta _{p_{1}}u-M_{2}\left(\Vert \nabla u\Vert ^{p_{2 ...
Vincenzo Ambrosio
wiley   +1 more source

Ground state sign-changing solution for a logarithmic Kirchhoff-type equation in $\mathbb{R}^{3}$

Electronic Journal of Qualitative Theory of Differential Equations
We investigate the following logarithmic Kirchhoff-type equation: \begin{equation*} \left(a+b\int_{\mathbb{R}^{3}}|\nabla u|^{2}+V(x)u^{2}dx\right)[-\Delta u+V(x)u]=|u|^{p-2}u\ln |u|,\qquad x\in\mathbb{R}^{3}, \end{equation*} where $a,b>0$ are constants,
Wei-Long Yang, Jia-Feng Liao
doaj   +1 more source

Generalized noncooperative Schrödinger–Kirchhoff–type systems in RN$\mathbb {R}^N$

Mathematische Nachrichten, Volume 297, Issue 6, Page 2092-2121, June 2024.
Abstract We consider a class of noncooperative Schrödinger–Kirchhof–type system, which involves a general variable exponent elliptic operator with critical growth. Under certain suitable conditions on the nonlinearities, we establish the existence of infinitely many solutions for the problem by using the limit index theory, a version of concentration ...
Nabil Chems Eddine, Dušan D. Repovš
wiley   +1 more source

Multiple Solutions of a Nonlocal Problem with Nonlinear Boundary Conditions

Discrete Dynamics in Nature and Society, Volume 2024, Issue 1, 2024.
In this article, we consider a class of nonlocal p(x)‐Laplace equations with nonlinear boundary conditions. When the nonlinear boundary involves critical exponents, using the concentration compactness principle, mountain pass lemma, and fountain theorem, we can prove the existence and multiplicity of solutions.
Jie Liu, Qing Miao, Rigoberto Medina
wiley   +1 more source

Solutions for fractional p ( x , ⋅ ) $p(x,\cdot )$ -Kirchhoff-type equations in R N $\mathbb{R}^{N}$

Journal of Inequalities and Applications
In this paper, we discuss the fractional p ( x , ⋅ ) $p(x,\cdot )$ -Kirchhoff-type equations M ( ∫ R N × R N 1 p ( x , y ) | u ( x ) − u ( y ) | p ( x , y ) | x − y | N + s p ( x , y ) d x d y ) ( − Δ p ( x , . ) ) s u + | u | p ¯ ( x ) − 2 u = f ( x , u
Lili Wan
doaj   +1 more source

Multiplicity Results for a (p1(x), p2(x))‐Laplacian Equation via Variational Methods

Journal of Mathematics, Volume 2024, Issue 1, 2024.
We prove the existence and multiplicity of nontrivial weak solutions for the following (p1(x), p2(x))‐Laplacian equation involving variable exponents: −div∇up1x−2∇u−div∇up2x−2∇u+up2x−2u=λhx,u,inΩ,u=0,on∂Ω. Using Ricceri’s variational principle, we show the existence of at least three weak solutions for the problem.
A. Rezvani, Dengfeng Lü
wiley   +1 more source

Existence of Multiple High‐Energy Solutions for a Kind of Superlinear Second‐Order Elliptic Equations

Journal of Mathematics, Volume 2024, Issue 1, 2024.
In this paper, we intend to consider infinitely many high energy solutions for a kind of superlinear Klein–Gordon–Maxwell systems. Under some suitable assumptions on the potential function and nonlinearity, by using variational methods and the method of Nehari manifold, we obtain the existence result of infinitely many high energy solutions for this ...
Fangfang Huang, Qiongfen Zhang, M. Palanivel   +2 more
wiley   +1 more source

Periodic and Antiperiodic Solutions for a Second‐Order Hamiltonian System With Nonlinearity Depending on Derivative

Journal of Function Spaces, Volume 2024, Issue 1, 2024.
Some existence results of periodic solution are obtained for a class of second‐order Hamiltonian systems with nonlinearity depending on derivative. We prove that there exists T0 > 0 such that, for any T < T0, the provided Hamiltonian system has a nontrivial T‐periodic and T/2‐antiperiodic solution via linking theorem and iteration method.
Wenxiong Chen, Shibo Liu, Wilfredo Urbina   +2 more
wiley   +1 more source

Multiplicity of ground state solutions for discrete nonlinear Schrodinger equations with unbounded potentials

Electronic Journal of Differential Equations, 2017
The discrete nonlinear Schrodinger equation is a nonlinear lattice system that appears in many areas of physics such as nonlinear optics, biomolecular chains and Bose-Einstein condensates.
Xia Liu, Tao Zhou, Haiping Shi
doaj