Existence and Multiplicity of Solutions to a p-Laplacian Equation with Nonlinear Boundary Condition
MetadataShow full metadata
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.
CitationPfluger, K. (1998). Existence and multiplicity of solutions to a p-Laplacian equation with nonlinear boundary condition. Electronic Journal of Differential Equations, 1998(10), pp. 1-13.
This work is licensed under a Creative Commons Attribution 4.0 International License.