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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 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

In this paper, we deal with a singular quasilinear critical elliptic equation of Lichnerowicz type involving the p-Laplacian operator. With the help of the subcritical approach from variational method, we obtain the non-existence,…

Analysis of PDEs · Mathematics 2020-04-24 Nanbo Chen , Xiaochun Liu

We investigate the existence of infinitely many radially symmetric solutions to the following problem $$(-\Delta_p)^s u=g(u) \ \ \textrm{ in } \ \ \mathbb{R}^N, \ \ u\in W^{s,p}(\mathbb{R}^N),$$ where $s\in (0,1)$, $2 \leq p < \infty$, $sp…

Analysis of PDEs · Mathematics 2021-05-25 Hamilton Bueno , Olimpio Miyagaki , Ailton Vieira

It is established existence, uniqueness and multiplicity of solutions for a quasilinear elliptic problem problems driven by $\Phi$-Laplacian operator. Here we consider the reflexive and nonreflexive cases using an auxiliary problem. In…

Analysis of PDEs · Mathematics 2017-09-19 M. L. M. Carvalho , J. V. Goncalves , Edcarlos D. da Silva , K. O. Silva

Using variational methods, we obtain several multiplicity results for double phase problems that involve variable exponents and a new type of critical growth. This new critical growth is better suited for double phase problems when compared…

Analysis of PDEs · Mathematics 2023-08-15 Hoang Hai Ha , Ky Ho

This work deals with the existence of at least two positive solutions for the class of quasilinear elliptic equations with cylindrical singularities and multiple critical nonlinearities that can be written in the form \begin{align*}…

Analysis of PDEs · Mathematics 2015-07-01 Ronaldo B. Assunção , Weler W. dos Santos , Olímpio H. Miyagaki

We establish some existence results for Schr\"odinger $p(x)$-Laplace equations in $\mathbb{R}^N$ with various potentials and critical growth of nonlinearity that may occur on some nonempty set, although not necessarily the whole space…

Analysis of PDEs · Mathematics 2018-07-12 Ky Ho , Yun-Ho Kim , Inbo Sim

The aim of this paper is to extend previous results regarding the multiplicity of solutions for quasilinear elliptic problems with critical growth to the variable exponent case. We prove, in the spirit of \cite{DPFBS}, the existence of at…

Analysis of PDEs · Mathematics 2009-12-18 Analía Silva

It is established some existence and multiplicity of solution results for a quasilinear elliptic problem driven by $\Phi$-Laplacian operator. One of these solutions is built as a ground state solution. In order to prove our main results we…

Analysis of PDEs · Mathematics 2017-03-28 M. L. M. Carvalho , J. V. Goncalves , C. Goulart , O. H. Miyagaki

In this paper, we are concern with the multiplicity of solutions for a p-Laplacian problem. A weaker super-quadratic assumptions is required on the nonlinearity. Under the weaker condition we give a new proof for the infinite solutions…

Analysis of PDEs · Mathematics 2014-12-01 Jing Zeng

By using a suitable topological argument based on cohomological linking and by exploiting a Trudinger-Moser inequality in fractional spaces recently obtained, we prove existence of multiple solutions for a problem involving the nonlinear…

Analysis of PDEs · Mathematics 2017-04-04 Kanishka Perera , Marco Squassina

In this paper, we investigate the existence of multiple periodic solutions for two classes of nonlinear difference systems involving $(\phi_1,\phi_2)$-Laplacian. First, by using an important critical point theorem due to B. Ricceri, we…

Dynamical Systems · Mathematics 2016-01-05 Xingyong Zhang , Liben Wang

In this paper, we are concerned with the multiplicity of nontrivial solutions for the following class of complex problems $$ (-i\nabla - A(\mu x))^{2}u= \mu |u|^{q-2}u + |u|^{2^{*}-2}u \ \mbox{in} \ \Omega, \ \ \ \ u \in…

Analysis of PDEs · Mathematics 2013-04-18 Claudianor O. Alves , Giovany M. Figueiredo

We prove new multiplicity results for some elliptic problems with critical exponential growth. More specifically, we show that the problems considered here have arbitrarily many solutions for all sufficiently large values of a certain…

Analysis of PDEs · Mathematics 2024-01-30 Kanishka Perera

We consider the boundary value problem $-\Delta_p u = \lambda c(x) |u|^{p-2}u + \mu(x) |\grad u|^p + h(x)$, $u \in W^{1,p}_0(\Omega) \cap L^{\infty}(\Omega)$, where $\Omega \subset \mathbb R^N$, $N \geq 2$, is a bounded domain with smooth…

Analysis of PDEs · Mathematics 2018-01-15 Colette De Coster , Antonio J. Fernández

In this paper, we consider a p-Laplacian equation in {R}^{N}with sign-changing potential and subcritical p-superlinear nonlinearity. By using the cohomological linking method for cones developed by Degiovanni and Lancelotti in 2007, an…

Analysis of PDEs · Mathematics 2010-11-25 Chungen Liu , Youquan Zheng

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

We consider Dirichlet elliptic equations driven by the sum of a $p$-Laplacian $(2<p)$ and a Laplacian. The conditions on the reaction term imply that the problem is resonant at both $\pm\infty$ and at zero. We prove an existence theorem…

Analysis of PDEs · Mathematics 2018-01-18 Nikolaos S. Papageorgiou , Vicenţiu D. Rădulescu , Dušan D. Repovš

We prove the existence of solutions for a class of quasilinear problems involving variable exponents and with nonlinearity having critical growth. The main tool used is the variational method, more precisely, Ekeland's Variational Principle…

Analysis of PDEs · Mathematics 2013-12-12 Claudianor O. Alves , Marcelo C. Ferreira