Existence Results for the p(x)-Laplacian with Nonlinear Boundary Condition
نویسندگان
چکیده
منابع مشابه
Existence and multiplicity of solutions to a p-Laplacian equation with nonlinear boundary condition
We study the nonlinear elliptic boundary value problem Au = f(x, u) in Ω , Bu = g(x, u) on ∂Ω , where A is an operator of p−Laplacian type, Ω is an unbounded domain in R with non-compact boundary, and f and g are subcritical nonlinearities. We show existence of a nontrivial nonnegative weak solution when both f and g are superlinear. Also we show existence of at least two nonnegative solutions ...
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Here Ω is a bounded domain in RN with smooth boundary, ∆pu = div(|∇u|p−2∇u) is the p-Laplacian, and ∂/∂ν is the outer normal derivative. In the linear case, that is for p = 2, this eigenvalue problem is known as the Steklov problem (see [3]). Problems of the form (1.1) appear in a natural way when one considers the Sobolev trace inequality. In fact, the immersionW1,p(Ω) ↪→ Lp(∂Ω) is compact, he...
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ژورنال
عنوان ژورنال: ISRN Applied Mathematics
سال: 2012
ISSN: 2090-5572
DOI: 10.5402/2012/727398