Multiple Positive Solutions for Semilinear Elliptic Equations with Sign-Changing Weight Functions in
نویسندگان
چکیده
منابع مشابه
Multiple Positive Solutions for Semilinear Elliptic Equations with Sign - Changing Weight Functions
and Applied Analysis 3 In order to describe our main result, we need to define Λ0 ( 2 − q ( p − q‖a‖L∞ ) 2−q / p−2 ( p − 2 ( p − q)‖b ‖Lq∗ ) S p 2−q /2 p−2 q/2 p > 0, 1.3 where ‖a‖L∞ supx∈RNa x , ‖b ‖Lq∗ ∫ RN |b x |qdx 1/q∗ and Sp is the best Sobolev constant for the imbedding of H1 R into L R . Theorem 1.1. Assume that a1 , b1 b2 hold. If λ ∈ 0, q/2 Λ0 , Ea,λb admits at least two positive solu...
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and Applied Analysis 3 Theorem 1.1. Assume that (A1) and (B1) hold. If λ ∈ 0,Λ0 , then Eλa,b admits at least one positive solution inH1 R . Associated with Eλa,b , we consider the energy functional Jλa,b inH1 R : Jλa,b u 1 2 ‖u‖H1 − λ q ∫ RN a x |u|dx − 1 p ∫
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In this article, we study the multiplicity of solutions for the semilinear elliptic equation −∆u + a(x)u = f(x, u), x ∈ Ω, u = 0, x ∈ ∂Ω, where Ω ⊂ RN (N ≥ 3), the potential a(x) satisfies suitable integrability conditions, and the primitive of the nonlinearity f is of super-quadratic growth near infinity and is allowed to change sign. Our super-quadratic conditions are weaker the usual super-q...
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In this paper, we study the multiplicity of positive solutions for the Laplacian systems with sign-changing weight functions. Using the decomposition of the Nehari manifold, we prove that an elliptic system has at least two positive solutions.
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Correspondence should be addressed to Tsing-San Hsu, [email protected] Received 8 September 2010; Accepted 18 October 2010 Academic Editor: Julio Rossi Copyright q 2010 Tsing-San Hsu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly c...
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ژورنال
عنوان ژورنال: Abstract and Applied Analysis
سال: 2011
ISSN: 1085-3375,1687-0409
DOI: 10.1155/2011/864296