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Electronic Journal of Differential Equations
Article . 2004
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zbMATH Open
Article . 2004
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Entire solutions of semilinear elliptic equations

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 2004Publisher:Southwest Texas State University, Department of Mathematics, San Marcos, TX; North Texas State University, Department of Mathematics, Denton, TXJournal:Electronic Journal of Differential Equations (issn: 1072-6691, Copyright policy )
Authors: Alexander Gladkov; Nickolai Slepchenkov;

Entire solutions of semilinear elliptic equations

Abstract

Summary: We consider existence of entire solutions of a semilinear elliptic equation \(\Delta u= k(x) f(u)\) for \(x \in \mathbb R^n\), \(n\geq 3\). Conditions of the existence of entire solutions have been obtained by different authors. We prove a certain optimality of these results and new sufficient conditions for the nonexistence of entire solutions.

Keywords

nonexistence., nonexistence, QA1-939, Nonlinear elliptic equations, Semilinear elliptic equation, entire solutions, Mathematics

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selected citations
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This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
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popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
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