Positive solutions of semilinear elliptic problems in unbounded domains
نویسندگان
چکیده
منابع مشابه
EXISTENCE OF POSITIVE SOLUTIONS FOR SOME NONLINEAR ELLIPTIC PROBLEMS IN UNBOUNDED DOMAINS OF Rn
This paper deals with a class of nonlinear elliptic equations in an unbounded domain D of Rn, n≥ 3, with a nonempty compact boundary, where the nonlinear term satisfies some appropriate conditions related to a certain Kato class K∞(D). Our purpose is to give some existence results and asymptotic behaviour for positive solutions by using the Green function approach and the Schauder fixed point t...
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Correspondence should be addressed to Faten Toumi, [email protected] Received 18 June 2010; Accepted 25 September 2010 Academic Editor: A. Mikelic Copyright q 2010 Faten Toumi. 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 cited. Thi...
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Palais-smale Approaches to Semilinear Elliptic Equations in Unbounded Domains
Let Ω be a domain in RN , N ≥ 1, and 2∗ = ∞ if N = 1, 2, 2∗ = 2N N−2 if N > 2, 2 < p < 2 ∗. Consider the semilinear elliptic problem −∆u+ u = |u|p−2u in Ω; u ∈ H 0 (Ω). Let H1 0 (Ω) be the Sobolev space in Ω. The existence, the nonexistence, and the multiplicity of positive solutions are affected by the geometry and the topology of the domain Ω. The existence, the nonexistence, and the multipli...
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ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 1985
ISSN: 0022-0396
DOI: 10.1016/0022-0396(85)90061-0