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Existence and multiplicity of solutions for an elliptic system with nonlinear boundary conditions

✍ Scribed by Xiaoming He; Wenming Zou

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
625 KB
Volume
71
Category
Article
ISSN
0362-546X

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✦ Synopsis

In this paper we prove the existence and multiplicity of solutions for the elliptic system

with nonlinear coupling at the smooth boundary given by

where Ω is a bounded domain of R N with smooth boundary, βˆ‚/βˆ‚Ξ½ is the outer normal derivative. The proofs are done under suitable assumptions on the Hamiltonian, and based on the local linking theorem and a multiple critical points theorem of the critical point theory.

πŸ“œ SIMILAR VOLUMES

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Let \(\Omega\) be a smooth bounded domain of \(\mathbb{R}^{n}, n \geqslant 3\), and let \(a(x)\) and \(f(x)\) be two smooth functions defined on a neighbourhood of \(\Omega\). First we study the existence of nodal solutions for the equation \(\Delta u+a(x) u=f(x)|u|^{4 /(n-2)} u\) on \(\Omega, u=0\)

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✍ Xiuchao Song; Weihua Wang; Peihao Zhao πŸ“‚ Article πŸ“… 2009 πŸ› Elsevier Science 🌐 English βš– 411 KB

This paper deals with the nonlinear elliptic equationu + u = f (x, u) in a bounded smooth domain Ω βŠ‚ R N with a nonlinear boundary value condition. The existence results are obtained by the sub-supersolution method and the Mountain Pass Lemma. And nonexistence is also considered.