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Related papers: Degenerate Schr{\"o}dinger-Kirchhoff $(p, N)$-Lapl…

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This paper deals with the existence and the asymptotic behavior of non-negative solutions for a class of stationary Kirchhoff problems driven by a fractional integro-differential operator $\mathcal L_K$ and involving a critical…

Analysis of PDEs · Mathematics 2014-10-27 Giuseppina Autuori , Alessio Fiscella , Patrizia Pucci

This article focuses on the study of the existence, multiplicity and concentration behavior of ground states as well as the qualitative aspects of positive solutions for a $(p, N)$-Laplace Schr\"{o}dinger equation with logarithmic…

Analysis of PDEs · Mathematics 2025-10-23 Deepak Kumar Mahanta , Tuhina Mukherjee , Patrick Winkert

In this paper, we establish a type of uniqueness and nondegeneracy results for positive solutions to the following nonlocal Kirchhoff equations \begin{eqnarray*} -\left(a+b\int_{\mathbb{R}^{3}}|\nabla u|^{2}\text{d} x\right)\Delta…

Analysis of PDEs · Mathematics 2020-03-12 Gongbao Li , Shuangjie Peng , Chang-Lin Xiang

For a class of Kirchhoff functional, we first give a complete classification with respect to the exponent $p$ for its $L^2$-normalized critical points, and show that the minimizer of the functional, if exists, is unique up to translations.…

Analysis of PDEs · Mathematics 2017-03-30 Xiaoyu Zeng , Yimin Zhang

The aim of this paper is to study the multiplicity of solutions for the following Kirchhoff type elliptic systems \begin{eqnarray*} \left\{ \arraycolsep=1.5pt \begin{array}{ll} -m\left(\sum^k_{j=1}\|u_j\|^2\right)\Delta…

Analysis of PDEs · Mathematics 2022-01-10 Shengbing Deng , Xingliang Tian

We prove the existence of infinitely many nonnegative solutions to the following nonlocal elliptic partial differential equation involving singularities \begin{align} (-\Delta)_{p(\cdot)}^{s}…

Analysis of PDEs · Mathematics 2021-08-26 Sekhar Ghosh , Debajyoti Choudhuri , Ratan Kr. Giri

We consider a nonlinear parametric Neumann problem driven by the anisotropic $(p,q)$-Laplacian and a reaction which exhibits the combined effects of a singular term and of a parametric superlinear perturbation. We are looking for positive…

Analysis of PDEs · Mathematics 2022-05-20 Nikolaos S. Papageorgiou , Vicenţiu D. Rădulescu , Dušan D. Repovš

We generalize two embedding theorems and investigate the existence and multiplicity of nontrivial solutions for a $(p,q)$-Laplacian coupled system with perturbations and two parameters $\lambda_1$ and $\lambda_2$ on locally finite graph. By…

Analysis of PDEs · Mathematics 2023-04-28 Ping Yang , Xingyong Zhang

The higher order Kirchhoff type equation $$\int_{\mathbb{R}^{2m}}(|\nabla^m u|^2 +\sum_{\gamma=0}^{m-1}a_{\gamma}(x)|\nabla^{\gamma}u|^2)dx \left((-\Delta)^m u+\sum_{\gamma=0}^{m-1}(-1)^\gamma \nabla^\gamma\cdot(a_\gamma (x)\nabla^\gamma…

Analysis of PDEs · Mathematics 2015-07-21 Liang Zhao , Ning Zhang

In this article, we are interested in semilinear, possibly degenerate elliptic equations posed on a general network, with nonlinear Kirchhoff-type conditions for its interior vertices and Dirichlet boundary conditions for the boundary ones.…

Analysis of PDEs · Mathematics 2025-09-17 Guy Barles , Olivier Ley , Erwin Topp

In this paper, we investigate the existence of weak solutions for a class of degenerate elliptic Dirichlet problems with critical nonlinearity and a logarithmic perturbation

Analysis of PDEs · Mathematics 2024-05-20 Hua Chen , Xin Liao , Ming Zhang

This paper is concerned with the multiplicity results to a class of $p$-Kirchhoff type elliptic equation with the homogeneous Neumann boundary conditions by an abstract linking lemma due to Br\'{e}zis and Nirenberg. We obtain the twofold…

Analysis of PDEs · Mathematics 2025-01-07 Weihua Wang

We establish some existence results for a class of critical elliptic problems with singular exponential nonlinearities. We do not assume any global sign conditions on the nonlinearity, which makes our results new even in the nonsingular…

Analysis of PDEs · Mathematics 2020-06-04 Shiqiu Fu , Kanishka Perera

In this paper we study the geometry of certain functionals associated to quasilinear elliptic boundary value problems with a degenerate nonlocal term of Kirchhoff type. Due to the degeneration of the nonlocal term it is not possible to…

Analysis of PDEs · Mathematics 2020-04-21 Leonelo Iturriaga , Eugenio Massa

The main purpose of this paper is to establish the existence of positive solutions to a class of quasilinear elliptic equations involving the (p-q)-Laplacian operator. We consider a nonlinearity that can be subcritical at infinity and…

Analysis of PDEs · Mathematics 2015-08-27 M. J. Alves , R. B. Assunção , O. H. Miyagaki

We study the following Kirchhoff equation $$- \left(1 + b \int_{\mathbb{R}^3} |\nabla u|^2 dx \right) \Delta u + V(x) u = f(x,u), \ x \in \mathbb{R}^3.$$ A special feature of this paper is that the nonlinearity $f$ and the potential $V$ are…

Analysis of PDEs · Mathematics 2019-09-25 Lin Li , Vicenţiu D. Rădulescu , Dušan D. Repovš

In this article, we deal with the following $p$-fractional Schr\"{o}dinger-Kirchhoff equations with electromagnetic fields and the Hardy-Littlewood-Sobolev nonlinearity: $$ M\left([u]_{s,A}^{p}\right)(-\Delta)_{p, A}^{s} u+V(x)|u|^{p-2}…

Analysis of PDEs · Mathematics 2024-01-12 Min Zhao , Yueqiang Song , Dušan D. Repovš

We consider the hyperbolic-parabolic singular perturbation problem for a nondegenerate quasilinear equation of Kirchhoff type with weak dissipation. This means that the dissipative term is multiplied by a coefficient b(t) which tends to 0…

Analysis of PDEs · Mathematics 2009-01-05 Marina Ghisi , Massimo Gobbino

The paper deals with the existence and uniqueness of a non-trivial solution to non-homogeneous $ p ( x ) -$laplacian equations, managed by non polynomial growth operator in the framework of variable exponent Sobolev spaces on Riemannian…

Analysis of PDEs · Mathematics 2020-06-09 Omar Benslimane , Ahmed Aberqi , Jaouad Bennouna

This article presents a comprehensive study of \textit{Kirchhoff-type Critical Elliptic Equations} involving $p$-sub-Laplacian Operators on the \textit{Heisenberg Group} $\mathcal{H}_{n}$. It delves into the mathematical framework of…

General Mathematics · Mathematics 2023-12-06 Subham De