Positive solutions of elliptic equations with nonlinear boundary conditions

This paper deals with the nonlinear elliptic equation − Δ u + u = f ( x , u ) in a bounded smooth domain Ω ⊂ R N with a nonlinear boundary value condition. The existence results are obtained by the sub–supersolution method and the Mountain Pass Lemma. And nonexistence is also considered.

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Veröffentlicht in:	Nonlinear analysis 2009, Vol.70 (1), p.328-334
Hauptverfasser:	Song, Xiuchao, Wang, Weihua, Zhao, Peihao
Format:	Artikel
Sprache:	eng
Schlagworte:	Coercive Exact sciences and technology Mathematical analysis Mathematics Mountain Pass Lemma Nonlinear boundary value condition Nonlinear elliptic equation Partial differential equations Sciences and techniques of general use Sub–supersolution Weakly lower semi-continuous
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Beschreibung
Zusammenfassung:	This paper deals with the nonlinear elliptic equation − Δ u + u = f ( x , u ) in a bounded smooth domain Ω ⊂ R N with a nonlinear boundary value condition. The existence results are obtained by the sub–supersolution method and the Mountain Pass Lemma. And nonexistence is also considered.
ISSN:	0362-546X 1873-5215
DOI:	10.1016/j.na.2007.12.003