Existence and Multiplicity of Solutions to a p-Laplacian Equation with Nonlinear Boundary Condition
Date
1998-04-10
Authors
Pfluger, Klaus
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
Abstract
We study the nonlinear elliptic boundary value problem
Au = ƒ(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 ℝN with non-compact boundary, and ƒ 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 when one of the two functions ƒ, g is sublinear and the other one is superlinear. The proofs are based on variational methods applied to weighted function spaces.
Description
Keywords
p-Laplacian, Nonlinear boundary condition, Variational methods, Unbounded domain, Weighted function space
Citation
Pfluger, K. (1998). Existence and multiplicity of solutions to a p-Laplacian equation with nonlinear boundary condition. <i>Electronic Journal of Differential Equations, 1998</i>(10), pp. 1-13.
Rights
Attribution 4.0 International