Related papers: Some quasilinear elliptic equations involving mult…
Existence and non-existence results are established for quasilinear elliptic problems with nonlinear boundary conditions and lack of compactness. The proofs combine variational methods with the geometrical feature, due to the competition…
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…
In this paper we develop a new theory for the existence, localization and multiplicity of positive solutions for a class of non-variational,quasilinear, elliptic systems. In order to do this, we provide a fairly general abstract framework…
We discuss the existence and regularity of solutions to a quasi-linear elliptic equation involving a Leray-Lions operator and a convection term with superlinear growth. In particular, equations involving the p-Laplacian are covered. This…
We prove the existence of one positive, one negative, and one sign-changing solution of a $p$-Laplacian equation on $\mathbb{R}^N$, with a $p$-superlinear subcritical term. Sign-changing solutions of quasilinear elliptic equations set on…
Boundary value problems for a class of quasilinear elliptic equations, with an Orlicz type growth and L^1 right-hand side are considered. Both Dirichlet and Neumann problems are contemplated. Existence and uniqueness of generalized…
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*}…
In this paper we study the nonlinear elliptic problem with p(x)-Laplacian (hemivariational inequality). We prove the existence of a nontrivial solution. Our approach is based on critical point theory for locally Lipschitz functionals due to…
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…
We consider a $(p,2)$-equation, that is, a nonlinear nonhomogeneous elliptic equation driven by the sum of a $p$-Laplacian and a Laplacian with $p>2$. The reaction term is $(p-1)$-linear but exhibits asymmetric behaviour at $\pm\infty$ and…
We show some examples for uniformly monotone operators arising in weak formulation of nonlinear elliptic and parabolic problems. Besides the classical $p$-Laplacian some other less known examples are given which might be of interest because…
We prove general a priori estimates of solutions of a class of quasilinear elliptic system on Carnot groups. As a consequence, we obtain several non existence theorems. The results are new even in the Euclidean setting.
The purpose of this paper is to study nonlinear singular parabolic equations with $p(x)$- Laplacian. Precisely, we consider the following problem and discuss the existence of a non-negative weak solution. \begin{align*} \frac{\partial…
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…
In the present paper, we study a class of quasilinear Choquard equations involving $N$-Laplacian and the nonlinearity with the critical exponential growth. We discuss the existence of positive solutions of such equations.
The global existence of weak solutions to a class of quasilinear parabolic equations with nonlinearities depending on first order terms and integrable data in a moving domain is investigated. The class includes the $p$-Laplace equation as a…
The aim of this paper is investigating the existence of weak solutions of the quasilinear elliptic model problem \[ \left\{\begin{array}{lr} - \divg (A(x,u)\, |\nabla u|^{p-2}\, \nabla u) + \dfrac1p\, A_t(x,u)\, |\nabla u|^p\ =\ f(x,u) &…
The paper is concerned with the existence of positive weak solutions for a new class of $\left( p,q\right) $-Laplacian elliptic systems in a bounded domain by means of the method of sub-super solutions. Particularly, we do not need any sign…
In this paper we study quasilinear elliptic systems given by \begin{equation*} \begin{aligned} -\Delta_{p_1}u_1 & =-|u_1|^{p_1-2}u_1 \quad && \text{in } \Omega,\newline -\Delta_{p_2}u_2 & =-|u_2|^{p_2-2}u_2 \quad && \text{in }…
We consider nonlinear elliptic problems involving a nonlocal operator: the square root of the Laplacian in a bounded domain with zero Dirichlet boundary conditions. For positive solutions to problems with power nonlinearities, we establish…