A remark on the existence of multiple solutions to a multiparameter nonlinear elliptic system

✍ Scribed by G.A. Afrouzi; S.H. Rasouli

• Publisher: Elsevier Science
• Year: 2009
• Tongue: English
• Weight: 645 KB
• Volume: 71
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/j.na.2008.10.118

✦ Synopsis

In this work, motivated by [T.F. Wu, The Nehari manifold for a semilinear elliptic system involving sign-changing weight function, Nonlinear. Anal. 68 (2008) 1733-1745], and using recent ideas from Brown and Wu [K.J. Brown, T.F. Wu, A semilinear elliptic system involving nonlinear boundary condition and sign changing weight function, J. Math. Anal. Appl. 337 (2008) 1326-1336], we prove the existence of nontrivial nonnegative solutions to the nonlinear elliptic system

Here ∆ p denotes the p-Laplacian operator defined by

∂n is the outer normal derivative, (λ, µ) ∈ R 2 \ {(0, 0)}, the weight m(x) is a bounded function with m ∞ > 0, and c(x) is a continuous function which changes sign in Ω.