A semilinear elliptic problem involving nonlinear boundary condition and sign-changing potential
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Date
2006-10-17
Authors
Wu, Tsung-fang
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University-San Marcos, Department of Mathematics
Abstract
In this paper, we study the multiplicity of nontrivial nonnegative solutions for a semilinear elliptic equation involving nonlinear boundary condition and sign-changing potential. With the help of the Nehari manifold, we prove that the semilinear elliptic equation:
-Δu + u = λƒ(x)|u|q-2u in Ω,
∂u/∂v = g(x)|u|p-2u on ∂Ω,
has at least two nontrivial nonnegative solutions for λ is sufficiently small.
Description
Keywords
Semilinear elliptic equations, Nehari manifold, Nonlinear boundary condition
Citation
Wu, T. F. (2006). A semilinear elliptic problem involving nonlinear boundary condition and sign-changing potential. <i>Electronic Journal of Differential Equations, 2006</i>(131), pp. 1-15.
Rights
Attribution 4.0 International