A universal bound for radial solutions of the quasilinear parabolic equation with p-Laplace operator

Existence of three solutions for a class of quasilinear elliptic systems involving the $p(x)$-Laplace operator

The aim of this paper is to obtain three weak solutions for the Dirichlet quasilinear elliptic systems on a bonded domain. Our technical approach is based on the general three critical points theorem obtained by Ricceri.

Three solutions for a class of quasilinear elliptic systems involving the p(x)-Laplace operator

* Correspondence: [email protected]. cn Institute of Mathematics, School of Mathematical Sciences, Nanjing Normal University, Jiangsu Nanjing 210046, China Full list of author information is available at the end of the article Abstract The existence of at least three weak solutions is established for a class of quasilinear elliptic systems involving the p(x)-Laplace operator with Neumann boundary ...

A Quasilinear Parabolic Equation With Inhomogeneous Density and Absorption

MULTIPLE SOLUTIONS FOR THE p−LAPLACE OPERATOR WITH CRITICAL GROWTH

In this paper we show the existence of at least three nontrivial solutions to the following quasilinear elliptic equation −∆pu = |u| ∗ u + λf(x, u) in a smooth bounded domain Ω of R with homogeneous Dirichlet boundary conditions on ∂Ω, where p = Np/(N − p) is the critical Sobolev exponent and ∆pu = div(|∇u|∇u) is the p−laplacian. The proof is based on variational arguments and the classical con...

EXISTENCE OF SOLUTIONS TO A PARABOLIC p(x)-LAPLACE EQUATION WITH CONVECTION TERM VIA L∞ ESTIMATES

This article is devoted to the study of the existence of weak solutions to an initial and boundary value problem for a parabolic p(x)-Laplace equation with convection term. Using the De Giorgi iteration technique, the authors establish the critical a priori L∞-estimates and thus prove the existence of weak solutions.