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Title: Mountain Pass Solutions and an Indefinite Superlinear Elliptic Problem on ℝ^N
Contributor(s): Du, Yihong  (author); Guo, Yuxia (author)
Publication Date: 2003
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Abstract: We consider the elliptic problem -Δu - λu = a(x)g(u), with a(x) sign-changing and g(u) behaving like u^p, p > 1. Under suitable conditions on g(u) and a(x), we extend the multiplicity, existence and nonexistence results known to hold for this equation on a bounded domain (with standard homogeneous boundary conditions) to the case that the bounded domain is replaced by the entire space ℝ^N. More precisely, we show that there exists Λ > 0 such that this equation on ℝ^N has no positive solution for λ > Λ, at least two positive solutions for λ ∈ (o,Λ), and at least one positive solution for λ ∈ (-∞,0]U{A}. Our approach is based on some descriptions of mountain pass solutions of semilinear elliptic problems on bounded domains obtained by a special version of the mountain pass theorem. These results are of independent interests.
Publication Type: Journal Article
Source of Publication: Topological Methods in Nonlinear Analysis, 22(1), p. 69-92
Publisher: Juliusz Schauder Center
Place of Publication: Torun, Poland
ISSN: 1230-3429
Field of Research (FOR): 010109 Ordinary Differential Equations, Difference Equations and Dynamical Systems
Socio-Economic Outcome Codes: 970101 Expanding Knowledge in the Mathematical Sciences
Peer Reviewed: Yes
HERDC Category Description: C1 Refereed Article in a Scholarly Journal
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