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:
has at least two nontrivial nonnegative solutions for is sufficiently small.
Submitted July 6, 2006. Published October 17, 2006.
Math Subject Classifications: 35J65, 35J50, 35J55.
Key Words: Semilinear elliptic equations; Nehari manifold; Nonlinear boundary condition.
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| Tsung-Fang Wu |
Department of Applied Mathematics
National University of Kaohsiung
Kaohsiung 811, Taiwan
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