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We develop a unified framework for a broad class of nonlocal elliptic problems, encompassing a wide spectrum of nonlocal terms, including the classical Kirchhoff and Carrier-type equations as particular cases, and nonlinearities having…

Analysis of PDEs · Mathematics 2026-03-25 L. Gasinski , H. Ramos Quoirin , J. Santos Junior , K. Silva

We obtain critical embeddings and the concentration-compactness principle for the anisotropic variable exponent Sobolev spaces. As an application of these results,we confirm the existence of and find infinitely many nontrivial solutions for…

Analysis of PDEs · Mathematics 2024-03-27 N. Chems Eddine , M. A. Ragusa , D. D. Repovš

This paper deals with the existence and multiplicity of solutions for a class of Kirchhoff type elliptic system involving the Trudinger-Moser exponential growth nonlinearities. We first study the existence of solutions for the following…

Analysis of PDEs · Mathematics 2022-10-06 Shengbing Deng , Xingliang Tian

We study a nonlocal parametric problem driven by the fractional Laplacian operator combined with a Kirchhoff-type coefficient and involving a critical nonlinearity term in the sense of Sobolev embeddings. Our approach is of variational and…

Analysis of PDEs · Mathematics 2021-04-26 Luigi Appolloni , Giovanni Molica Bisci , Simone Secchi

We investigate the existence, multiplicity and concentration of nontrivial solutions for the following fractional magnetic Kirchhoff equation with critical growth: \begin{equation*} \left(a\varepsilon^{2s}+b\varepsilon^{4s-3}…

Analysis of PDEs · Mathematics 2019-07-24 Vincenzo Ambrosio

This paper is devoted to the study of the existence of positive and bounded solutions for a Schr\"odinger type equation defined on the entire Euclidean space, involving a general integro-differential operator. We consider the case where the…

Analysis of PDEs · Mathematics 2026-04-10 Ronaldo C. Duarte , Diego Ferraz

In this paper, we show the existence of non-trivial solutions to very general elliptic systems with critical non-linearities in the sense of embeddings in Orlicz-Sobolev spaces. This allows to consider non-linearities which do not have…

Analysis of PDEs · Mathematics 2025-03-20 Pablo Ochoa

We show an abstract critical point theorem about existence of infinitely many critical orbits to strongly indefinite functionals with sign-changing nonlinear part defined on a dislocation space with a discrete group action. We apply the…

Analysis of PDEs · Mathematics 2025-06-17 Federico Bernini , Bartosz Bieganowski , Daniel Strzelecki

In this work, we study the existence and multiplicity of solutions for a class of problems involving the $\phi$-Laplacian operator in a bounded domain, where the nonlinearity has a critical growth. The main tool used is the variational…

Analysis of PDEs · Mathematics 2015-04-06 Jefferson A. Santos

We study the existence of nonnegative solutions to the following nonlocal elliptic problem involving singularity \begin{align} \mathfrak{M}\left(\int_{Q}\frac{|u(x)-u(y)|^p}{|x-y|^{N+ps}}dxdy\right)(-\Delta)_{p}^{s}…

Analysis of PDEs · Mathematics 2024-06-18 Sekhar Ghosh , Debajyoti Choudhuri , Alessio Fiscella

In this paper we study logarithmic double phase problems with variable exponents involving nonlinearities that have generalized critical growth. We first prove new continuous and compact embedding results in order to guarantee the…

Analysis of PDEs · Mathematics 2025-07-21 Rakesh Arora , Ángel Crespo-Blanco , Patrick Winkert

In this paper, we are interested in the following critical Kirchhoff type elliptic equation with a logarithmic perturbation \begin{equation}\label{eq0} \begin{cases} -\left(1+b\int_{\Omega}|\nabla{u}|^2\mathrm{d}x\right) \Delta{u}=\lambda…

Analysis of PDEs · Mathematics 2025-05-01 Qian Zhang , Yuzhu Han

We study a class of Schr\"{o}dinger-Kirchhoff system involving critical exponent. We aim to find suitable conditions to assure the existence of a positive ground state solution of Nehari-Poho\u{z}aev type $u_{\varepsilon}$ with exponential…

Analysis of PDEs · Mathematics 2023-05-29 Anmin Mao , Qian Zhang

We obtain a critical imbedding and then, concentration-compactness principles for fractional Sobolev spaces with variable exponents. As an application of these results, we obtain the existence of many solutions for a class of critical…

Analysis of PDEs · Mathematics 2019-09-23 Ky Ho , Yun-Ho Kim

This paper is concerned with the multiplicity of nontrivial solutions in an Orlicz-Sobolev space for a nonlocal problem with critical growth, involving N-functions and theory of locally Lispchitz continuous functionals.

Analysis of PDEs · Mathematics 2015-04-06 Giovany M. Figueiredo , Jefferson A. Santos

In this paper we investigate a class of elliptic problems involving a nonlocal Kirchhoff type operator with variable coefficients and data changing its sign. Under appropriated conditions on the coefficients, we have shown existence and…

Analysis of PDEs · Mathematics 2017-12-06 Camil S. Z. Redwan , João R. Santos Júnior , Antonio Suárez

In this paper we establish, using variational methods combined with the Moser-Trudinger inequality, existence and multiplicity of weak solutions for a class of critical fractional elliptic equations with exponential growth without a…

Analysis of PDEs · Mathematics 2020-04-07 Hamilton Bueno , Eduardo Huerto Caqui , Olimpio Miyagaki

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

We consider a nonlocal differential equation of Kirchhoff type with a convolution coefficient involving variable growth. The novelty of our work lies in allowing a variable exponent in the nonlocal term. By relating the variable growth…

Analysis of PDEs · Mathematics 2026-02-17 Christopher S. Goodrich , Gabriel Nakhl

We prove the existence of infinitely many nontrivial weak periodic solutions for a class of fractional Kirchhoff problems driven by a relativistic Schr\"odinger operator with periodic boundary conditions and involving different types of…

Analysis of PDEs · Mathematics 2019-07-02 Vincenzo Ambrosio