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We study the existence and regularity of weak solutions to the following quasilinear elliptic system: \[ -\mathrm{div}(A_k(x, u_k) |\nabla u_k|^{p_k - 2} \nabla u_k) + \dfrac{1}{p_k} D_s A_k(x, u_k) |\nabla u_k|^{p_k} = g_k(x, u) \quad…

Analysis of PDEs · Mathematics 2026-02-24 Annamaria Canino , Simone Mauro

In this paper, we establish existence and multiplicity of solutions for the following class of quasilinear field equation $$ -\Delta u+V(x)u-\Delta_{p}u+W'(u)=0, \,\,\, \mbox{in} \,\,\, \mathbb{R}^{N}, \eqno{(P)} $$ where…

Analysis of PDEs · Mathematics 2017-02-16 Claudianor O. Alves , Alan C. B. dos Santos

We investigate the existence, non-existence, and multiplicity of positive solutions to a class of quasilinear Schrodinger equations with a prescribed mass condition in higher dimensions. Using the dual approach, the equation is transformed…

Analysis of PDEs · Mathematics 2024-11-26 Ayesha Baig , Li Zhouxin

We prove the existence of weak solutions for the one obstacle problem associated with a class of quasilinear wave equations in one space dimension, extending previous results obtained in the linear case, and we also address the two…

Analysis of PDEs · Mathematics 2026-04-02 João Paulo Dias , Wladimir Neves , José Francisco Rodrigues

We investigate the multiplicity of nontrivial weak solutions for a class of complex equations. This class of problems are related with the existence of solitary waves for a nonlinear Sch\"{o}dinger equation. The main result is established…

Analysis of PDEs · Mathematics 2013-04-19 Claudianor O. Alves , Giovany M. Figueiredo

Multiplicity results are proved for solutions both with positive and negative energy, as well as nonexistence results, of a generalized quasilinear Schr\"odinger potential free equation in the entire R^N involving a nonlinearity which…

Analysis of PDEs · Mathematics 2023-12-14 Laura Baldelli , Roberta Filippucci

This paper addresses a class of elliptic problems involving the superposition of nonlinear fractional operators with the critical Sobolev exponent in the sublinear regimes. We establish the existence of infinitely many nontrivial weak…

Analysis of PDEs · Mathematics 2026-02-17 Souvik Bhowmick , Sekhar Ghosh , Vishvesh Kumar

In this paper, we obtain infinitely many solutions for a class of quasilinear Schr\"{o}dinger-Poisson system which is coupled by a Schr\"{o}dinger equation of $p$-Laplacian and a Poisson equation of $q$-Laplacian, involving with concave and…

Analysis of PDEs · Mathematics 2025-09-22 Yao Du , Jiahao Peng

We establish the existence of multiple solutions for singular quasilinear elliptic problems with a precise sign information: two opposite constant sign solutions and a nodal solution. The approach combines sub-supersolutions method and…

Analysis of PDEs · Mathematics 2023-10-30 Dumitru Motreanu , Abdelkrim Moussaoui

A fourth-order elliptic problem of Leray-Lions type is considered for combined nonlinearities and Sobolev-critical growth with Navier and Dirichlet boundary conditions. By combining variational methods and critical point theory, the…

Analysis of PDEs · Mathematics 2025-11-04 Angelo Guimarães , Edcarlos Domingos da Silva , Eduardo. H. Gomes Tavares , Jin-Yun Yuan

We establish the multiplicity of positive solutions to a quasilinear Neumann problem in expanding balls and hemispheres with critical exponent in the boundary condition.

Analysis of PDEs · Mathematics 2016-12-05 Aleksandr Enin

In this study, we devote our attention to the question of clarifying the existence of a weak solution to a class of quasilinear double-phase elliptic equations with logarithmic convection terms under some appropriate assumptions on data.…

Analysis of PDEs · Mathematics 2024-01-05 Minh-Phuong Tran , Thanh-Nhan Nguyen

Critical Sobolev-type inequality for a class of weighted Sobolev spaces on the entire space is established. We also investigate the existence of extremal function for the associated variational problem. As an application, we prove the…

Analysis of PDEs · Mathematics 2024-06-28 José Francisco de Oliveira , Jeferson Silva

We provide a direct proof of existence and uniqueness of weak solutions to a broad family of strongly nonlinear elliptic equations with lower order terms. The leading part of the operator satisfies general growth conditions settling the…

Analysis of PDEs · Mathematics 2023-03-16 Iwona Chlebicka , Arttu Karppinen , Ying Li

We are concerned with nonexistence results of nonnegative weak solutions for a class of quasilinear parabolic problems with a potential on complete noncompact Riemannian manifolds. In particular, we highlight the interplay between the…

Analysis of PDEs · Mathematics 2015-02-27 P. Mastrolia , D. D. Monticelli , F. Punzo

We prove the existence of multiple signed bounded solutions for a quasilinear elliptic equation with concave and convex nonlinearities. For this, we use a variational approach in an intersection Banach space indroduced by Candela and…

Analysis of PDEs · Mathematics 2024-03-27 Federica Mennuni , Addolorata Salvatore

We study a boundary-value quasilinear elliptic problem on a generic time scale. Making use of the fixed-point index theory, sufficient conditions are given to obtain existence, multiplicity, and infinite solvability of positive solutions.

Analysis of PDEs · Mathematics 2007-10-08 Moulay Rchid Sidi Ammi , Delfim F. M. Torres

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

In this paper we analyze the existence of large positive radial solutions to some quasilinear elliptic systems. Also, a non-radially symmetric solution is obtained by using a lower and upper solution method. The equations are coupled by…

Classical Analysis and ODEs · Mathematics 2011-05-16 Dragos-Patru Covei

Mountain pass in a suitable Orlicz space is employed to prove the existence of soliton solutions for a quasilinear Schr\"{o}dinger equation involving critical exponent in ${\BR}^N$. These equations contain strongly singular nonlinearities…

Analysis of PDEs · Mathematics 2007-05-23 Abbas Moameni