Existence of solutions for p(x) -Laplacian dirichlet problem

By Xianling Fan, Qihu Zhang. 2003

879 citations recorded by the source corpus.

This paper presents several sufficient conditions for the existence of solutions for the Dirichlet problem of p(x)-Laplacian {-div(|∇u|p(x)-2∇u) = f(x,u), x ∈ Ω, u = 0, x ∈ ∂Ω. Especially, an existence criterion for infinite many pairs of solutions for the problem is obtained. The discussion is based on the theory of the spaces Lp(x)(Ω) and W01, p(x)(Ω).

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/bbf30ec2f9bf0b4dac32b8764a2fe10732a29882

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

The concentration-compactness principle for variable exponent spaces and applications (2009, neutral): “See, for instance [5, 6, 8, 13, 14] and references therein.”
A multiplicity result for a nonlinear degenerate problem arising in the theory of electrorheological fluids (2006, background): “3 in [9] problem (6) has at least a weak solution in the particular case a(x, ξ) = |ξ|p(x)−1ξ.”
Existence of positive solutions for a class of p(x)-Laplacian systems ✩ (2007, neutral): “Many results have been obtained on this kind of problems, for example [1–3,6–13,16,18].”
A pocket guide to nonlinear differential equations in Musielak–Orlicz spaces (2018, background): “Since the setting is carefully examined and broad range of problems is already addressed, we mention only a few attempts to basic properties of PDEs such as existence [75, 93, 148, 174], regularity results [1, 2], maximal principle [118], and nonexistence [4, 83].”
The Dirichlet Energy Integral and Variable Exponent Sobolev Spaces with Zero Boundary Values (2006, neutral): “has been studied by many authors see for example [3, 4, 16 ] and their references.”