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Multiplicity of solutions for biharmonic elliptic systems involving critical nonlinearity

Dengfeng Lu|Jianhai Xiao
대한수학회 (The Korean Mathematical Society)|2013.09|대한수학회보 (Bulletin of the KMS)|제50권 제5호|pp. 1693-1710

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참고문헌

키워드

variational methodcritical Sobolev exponentmultiple solutionsbiharmonic elliptic system
주제분류수학

초록

In this paper, we consider the biharmonic elliptic systems of the form [수식] where Ω ⊂ RN is a bounded domain with smooth boundary Ω, △2 is the biharmonic operator, N ≥ 5, 2 ≤ q < 2∗, 2∗ = 2N N−4 denotes the critical Sobolev exponent, F ∈ C1(R2, R+) is homogeneous function of degree 2∗. By using the variational methods and the Ljusternik-Schnirelmann theory, we obtain multiplicity result of nontrivial solutions under certain hypotheses on λ and δ. .

Abstract

In this paper, we consider the biharmonic elliptic systems of the form [수식] where Ω ⊂ RN is a bounded domain with smooth boundary Ω, △2 is the biharmonic operator, N ≥ 5, 2 ≤ q < 2∗, 2∗ = 2N N−4 denotes the critical Sobolev exponent, F ∈ C1(R2, R+) is homogeneous function of degree 2∗. By using the variational methods and the Ljusternik-Schnirelmann theory, we obtain multiplicity result of nontrivial solutions under certain hypotheses on λ and δ.

참고문헌 (23)

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