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We establish conditions for nonexistence of global solutions for a class of quasilinear parabolic problems with a potential on complete, non-compact Riemannian manifolds, including the Porous Medium Equation and the p-Laplacian with a…

Analysis of PDEs · Mathematics 2025-11-21 Dorothea-Enrica von Criegern , Gabriele Grillo , Dario Monticelli

In this paper, a critical fourth-order Kirchhoff type elliptic equation with a subcritical perturbation is studied. The main feature of this problem is that it involves both a nonlocal coefficient and a critical term, which bring essential…

Analysis of PDEs · Mathematics 2023-05-25 Qian Zhang , Yuzhu Han

This paper is focused on the solvability of a family of nonlinear elliptic systems defined in $\mathbb{R}^N$. Such equations contain Hardy potentials and Hardy-Sobolev criticalities coupled by a possible critical Hardy-Sobolev term. That…

Analysis of PDEs · Mathematics 2023-06-22 Rafael López-Soriano , Alejandro Ortega

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

This paper deals with the Klein-Gordon-Maxwell system in a bounded spatial domain. We study the existence of solutions having a specific form, namely standing waves in equilibrium with a purely electrostatic field. We prescribe Dirichlet…

Analysis of PDEs · Mathematics 2008-12-17 Pietro d'Avenia , Lorenzo Pisani , Gaetano Siciliano

We study the existence of bound and ground states for a class of nonlinear elliptic systems in $\mathbb{R}^N$. These equations involve critical power nonlinearities and Hardy-type singular potentials, coupled by a term containing up to…

Analysis of PDEs · Mathematics 2021-07-09 Eduardo Colorado , Rafael López-Soriano , Alejandro Ortega

This work is devoted to infinite-energy solutions of semi-linear wave equations in unbounded smooth domains of $\mathbb{R}^3$ with fractional damping of the form $(-\Delta_x+1)^\frac{1}{2}\partial_t u$. The work extends previously known…

Analysis of PDEs · Mathematics 2015-11-17 Anton Savostianov

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

This paper is concerned with a class of quasilinear elliptic equations involving some potentials related to the Caffarelli-Korn-Nirenberg inequality. We prove the local boundedness and H\"older continuity of weak solutions by using the…

Analysis of PDEs · Mathematics 2020-09-01 Le Cong Nhan , Ky Ho , Le Xuan Truong

We establish existence and regularity of positive solutions for a class of quasilinear elliptic systems with singular and superlinear terms. The approach is based on sub-supersolution methods for systems of quasilinear singular equations…

Analysis of PDEs · Mathematics 2016-04-26 Brahim Khodja , Abdelkrim Moussaoui

In this work we use variational methods to show the existence of weak solutions for a nonlinear problem of the type elliptic. This problem was initially study by the authors Ahmad, Lazer and Paul (see \cite{ALP}) considering the space…

Analysis of PDEs · Mathematics 2009-05-08 Antonio Ronaldo G. Garcia , Moises D. dos Santos , Adriao D. D. Neto

In this paper, we study the existence and multiplicity of weak solutions to a general type of Kirchhoff equations in magnetic fractional Orlicz-Sobolev spaces. Specifically, we appeal to Critical Point Theory to prove the existence of…

Analysis of PDEs · Mathematics 2022-07-15 Pablo Ochoa

In this work, we investigate the existence of multiple positive solutions for a weakly coupled system of nonlinear elliptic equations governed by Pucci extremal operators. Specifically, we consider the system: \[ \begin{cases}…

Analysis of PDEs · Mathematics 2026-03-27 Karan Rathore , Mohan Mallick

We consider the Euler system set on a bounded convex planar domain, endowed with impermeability boundary conditions. This system is a model for the barotropic mode of the Primitive Equations on a rectangular domain. We show the existence of…

Analysis of PDEs · Mathematics 2013-08-19 Claude Bardos , Francesco Di Plinio , Roger Temam

In this work we consider a system of quasilinear elliptic equations driven by an anisotropic $p$-Laplacian. The lower-order nonlinearities are in potential form and exhibit critical Sobolev growth. We exhibit conditions on the coefficients…

Analysis of PDEs · Mathematics 2024-01-01 Mathew Gluck

In this paper, using the theory developed in [8], we obtain some results of a totally new type about a class of non-local problems. Here is a sample: Let $\Omega\subset {\bf R}^n$ be a smooth bounded domain, with $n\geq 4$, let $a, b,…

Analysis of PDEs · Mathematics 2014-09-23 Biagio Ricceri

In this paper, we study the solvability of the nonlinear Dirichlet problem with sum of the operators of independent non standard growths in a bounded domain $\Omega \subset \mathbb{R}^{n}$. We obtain sufficient conditions and show the…

Analysis of PDEs · Mathematics 2018-03-01 Uğur Sert , Kamal Soltanov

We investigate a class of Kirchhoff type equations involving a combination of linear and superlinear terms as follows: \begin{equation*} -\left( a\int_{\mathbb{R}^{N}}|\nabla u|^{2}dx+1\right) \Delta u+\mu V(x)u=\lambda…

Analysis of PDEs · Mathematics 2024-06-19 Juntao Sun , Kuan-Hsiang Wang , Tsung-fang Wu

By means of a recent Birkhoff-Kellogg type theorem, we discuss the solvability of a fairly general class of parameter-dependent fourth order retarded differential equations subject to functional boundary conditions. We seek solutions within…

Classical Analysis and ODEs · Mathematics 2024-10-16 Alessandro Calamai , Gennaro Infante

The purpose of this paper is to study the indefinite Kirchhoff type problem: \begin{equation*} \left\{ \begin{array}{ll} M\left( \int_{\mathbb{R}^{N}}(|\nabla u|^{2}+u^{2})dx\right) \left[ -\Delta u+u\right] =f(x,u) & \text{in…

Analysis of PDEs · Mathematics 2014-08-26 Juntao Sun , Tsung-fang Wu