Existence of solutions for a boundary problem involving p(x)-biharmonic operator

By Abdelrachid El Amrouss, Anass Ourraoui. 2012

70 citations recorded by the source corpus.

In this paper, we establish the existence of at least three solutions to a boundary problem involving the p(x)-biharmonic operator. Our technical approach is based on theorem obtained by B. Ricceri's variational principle and local mountain pass theorem without (Palais-Smale) condition. p(x)−2 u = f(x, u) + λg(x, u) in , Bu = T u = 0 on ∂, here is a bounded open domain in R N with smooth boundary ∂, � 2(x) u = �(| �u | p(x)−2 �u) is the p(x)−biharmonic with p ∈ C(), p(x) > 1, λ ∈ R , a ∈ L ∞ () such that infx∈ a(x) = a − > 0. Bu = T u = 0 denotes the following boundary conditions:

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/5d67c9fbf9eac29f489b4137346502c78c531b50

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

On a p(x)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varvec{p(x)}$$\end{document}-biharmonic problem with singula (2017, background): “More precisely, we have the following result (see [10]).”