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- W2548192511 abstract "We consider the elliptic problem $$ -Delta u-lambda u=a(x) g(u), $$ 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 $mathbb R^N$. More precisely, we show that there exists $Lambda> 0$ such that this equation on $mathbb R^N$ has no positive solution for $lambda> Lambda$, at least two positive solutions for $lambdain (0,Lambda)$, and at least one positive solution for $lambdain (-infty,0]cup{Lambda}$. 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." @default.
- W2548192511 created "2016-11-11" @default.
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- W2548192511 date "2003-09-01" @default.
- W2548192511 modified "2023-09-25" @default.
- W2548192511 title "Mountain pass solutions and an indefinite superlinear elliptic problem on $mathbb R^{mathbb N}$" @default.
- W2548192511 doi "https://doi.org/10.12775/tmna.2003.028" @default.
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