English
Related papers

Related papers: Polyharmonic Kirchhoff problems involving exponent…

200 papers

We prove the existence of Cantor families of small amplitude, linearly stable, quasi-periodic solutions of quasi-linear autonomous Hamiltonian generalized KdV equations. We consider the most general quasi-linear quadratic nonlinearity. The…

Analysis of PDEs · Mathematics 2016-07-12 Filippo Giuliani

The existence of a nontrivial solution is proved for a class of quasilinear elliptic equations involving, as principal part, either the p-Laplace operator or the operator related to the p-area functional, and a nonlinearity with p-linear…

Analysis of PDEs · Mathematics 2018-03-19 Silvia Cingolani , Marco Degiovanni , Giuseppina Vannella

In this paper we develop an analogue of the Berkovich analytification for non-necessarily algebraic complex spaces. We apply this theory to generalize to arbitrary compact K\"ahler manifolds a result of Chi Li, proving that a stronger…

Differential Geometry · Mathematics 2025-09-22 Pietro Mesquita-Piccione

We study degenerate complex Monge-Amp\`ere equations of the form $(\omega+dd^c \varphi)^n = e^{t \varphi} \mu$ where $\omega$ is a big semi-positive form on a compact K\"ahler manifold $X$ of dimension $n$, $t \in \R^+$, and $\mu=f\omega^n$…

Algebraic Geometry · Mathematics 2008-09-24 Philippe Eyssidieux , Vincent Guedj , Ahmed Zeriahi

The objective of this manuscript is to enquire for the solvability of a specific type of non-linear quadratic integral equations via the interesting notion of measure of non-compactness. Firstly, we inquire into couple of exciting fixed…

Functional Analysis · Mathematics 2020-08-17 Surajit Karmakar , Hiranmoy Garai , Lakshmi Kanta Dey , Ankush Chanda

In this paper, we investigate the existence of nontrivial weak solutions to a class of elliptic equations ($\mathscr{P}$) involving a general nonlocal integrodifferential operator $\mathscr{L}_{\mathcal{A}K}$, two real parameters, and two…

Analysis of PDEs · Mathematics 2020-03-31 Lauren Maria Mezzomo Bonaldo , Olmpio Hiroshi Miyagaki , Elard Jurez Hurtado

In this paper, we consider a fractional p-Laplacian system of equations in the entire space RN with doubly critical singular nonlinearities involving a local critical Sobolev term together with a nonlocal Choquard critical term; the problem…

Analysis of PDEs · Mathematics 2024-12-16 Ronaldo B. Assunção , Olímpio H. Miyagaki , Rafaella F. S. Siqueira

In this paper, we are concerned with the Neumann problem for a class of quasilinear stationary Kirchhoff-type potential systems, which involves general variable exponents elliptic operators with critical growth and real positive parameter.…

Analysis of PDEs · Mathematics 2023-03-06 Nabil Chems Eddine , Dušan D. Repovš

We apply a topological method to prove existence of positive solutions for the nonlineair Choquard equation with upper critical exponent in the sense of Hardy-Littlewood-Sobolev inquality on bounded domains having nontrivial homology group.

Analysis of PDEs · Mathematics 2025-02-10 Mohammed Ali Mohammed Alghamdi , Hichem Chtioui

Given (M, g0) we consider the problem -{\epsilon}^2Delta_{g0+h}u + u = (u+)^{p-1} with ({\epsilon}, h) \in (0, {\epsilon}0) \times B{\rho}. Here B{\rho} is a ball centered at 0 with radius {\rho} in the Banach space of all Ck symmetric…

Analysis of PDEs · Mathematics 2010-12-30 Marco G. Ghimenti , Anna Maria Micheletti

In this article, we study a double-phase variable-exponent Kirchhoff problem and show the existence of at least three solutions. The proposed model, as a generalization of the Kirchhoff equation, is interesting since it is driven by a…

Analysis of PDEs · Mathematics 2025-07-31 Mustafa Avci

This work resolves the open problem of strong singularity ($\alpha(z)> 1$) in nonlocal Kirchhoff-type equations with variable exponents through five original theorems that collectively establish a comprehensive theory. Beginning with…

Analysis of PDEs · Mathematics 2026-03-31 M. H. M. Rashid

This paper is devoted to study a fractional Choquard problem with slightly subcritical exponents on bounded domains. When the exponent of the convolution type nonlinearity tends to the fractional critical one in the sense of…

Analysis of PDEs · Mathematics 2023-02-07 Marco G. Ghimenti , Min Liu , Zhongwei Tang

We establish a continuous embedding $W^{s(\cdot),2}(\Omega)\hookrightarrow L^{\alpha(\cdot)}(\Omega)$, where the variable exponent $\alpha(x)$ can be close to the critical exponent $2_{s}^*(x)=\frac{2N}{N-2\bar{s}(x)}$, with…

Analysis of PDEs · Mathematics 2022-04-29 Jiabin Zuo , Debajyoti Choudhuri , Dušan D. Repovš

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

The purpose of this paper is to present a class of particular solutions of a C(2,1) conformally invariant nonlinear Klein-Gordon equation by symmetry reduction. Using the subgroups of similitude group reduced ordinary differential equations…

solv-int · Physics 2009-10-31 F. Gungor

In this paper, the following critical biharmonic elliptic problem \begin{eqnarray*} \begin{cases} \Delta^2u= \lambda u+\mu u\ln u^2+|u|^{2^{**}-2}u, &x\in\Omega,\\ u=\dfrac{\partial u}{\partial \nu}=0, &x\in\partial\Omega \end{cases}…

Analysis of PDEs · Mathematics 2022-11-22 Qi Li , Yuzhu Han , Tianlong Wang

In this paper, we consider Kirchhoff-Schrodinger equations with singular exponential nonlinearities in R^4,using singular Adams inequality and variational techniques, we get the existence of ground state solutions. Moreover, we also get the…

Analysis of PDEs · Mathematics 2019-10-08 Yanjun Liu , Shijie Qi

We investigate the existence of two nontrivial solutions for a poly-Laplacian system involving concave-convex nonlinearities and parameters with Dirichlet boundary condition on locally finite graphs. By using the mountain pass theorem and…

Analysis of PDEs · Mathematics 2023-12-27 Ping Yang , Xingyong Zhang

In the present work we are concerned with the following Kirchhoff-Choquard-type equation $$-M(||\nabla u||_{2}^{2})\Delta u +Q(x)u + \mu(V(|\cdot|)\ast u^2)u = f(u) \mbox{ in } \mathbb{R}^2 , $$ for $M: \mathbb{R} \rightarrow \mathbb{R}$…

Analysis of PDEs · Mathematics 2025-05-28 Eduardo de Souza Böer , Olímpio Hiroshi Miyagaki , Patrizia Pucci