Please use this identifier to cite or link to this item:
https://hdl.handle.net/1959.11/3170
Title: | Mountain Pass Solutions and an Indefinite Superlinear Elliptic Problem on ℝ^N | Contributor(s): | Du, Yihong (author) ; Guo, Yuxia (author) | Publication Date: | 2003 | Handle Link: | https://hdl.handle.net/1959.11/3170 | 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: | Poland | ISSN: | 1230-3429 | Fields of Research (FoR) 2008: | 010109 Ordinary Differential Equations, Difference Equations and Dynamical Systems | Socio-Economic Objective (SEO) 2008: | 970101 Expanding Knowledge in the Mathematical Sciences | Peer Reviewed: | Yes | HERDC Category Description: | C1 Refereed Article in a Scholarly Journal | Publisher/associated links: | http://www.tmna.ncu.pl/files/v22n1-04.pdf |
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Appears in Collections: | Journal Article School of Science and Technology |
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