This paper is concerned with the existence and multiplicity of positive solutions of the equation - Delta u + u = u(p-1), 2 < p < 2* 2N/N-2, with Dirichlet zero data, in an unbounded smooth domain Omega subset of R-N having unbounded boundary. Under the assumptions: (h(1)) there exists tau(1), tau(2),...,tau(k) is an element of R+\{0}, 1 <= k <= N - 2, such that (x(1), x(2),...,x(N)) is an element of Omega double left right arrow (x(1),...,x(i-1), x(i) + tau(i),...,x(N)) is an element of Omega, for all i = 1, 2,...,k, (h(2)) there exists R is an element of R+\{0} such that R-N\ Omega subset of {(x1, x2,...,x(N)) is an element of R-N: Sigma(N)(j=k+1) x(j)(2) <= R-2} the existence of at least k + 1 solutions is proved.

Cerami, G., Molle, R., Passaseo, D. (2007). Positive solutions of semilinear elliptic problems in unbounded domains with unbounded boundary. ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE, 24(1), 41-60 [10.1016/j.anihpc.2005.09.007].

Positive solutions of semilinear elliptic problems in unbounded domains with unbounded boundary

MOLLE, RICCARDO;
2007-01-01

Abstract

This paper is concerned with the existence and multiplicity of positive solutions of the equation - Delta u + u = u(p-1), 2 < p < 2* 2N/N-2, with Dirichlet zero data, in an unbounded smooth domain Omega subset of R-N having unbounded boundary. Under the assumptions: (h(1)) there exists tau(1), tau(2),...,tau(k) is an element of R+\{0}, 1 <= k <= N - 2, such that (x(1), x(2),...,x(N)) is an element of Omega double left right arrow (x(1),...,x(i-1), x(i) + tau(i),...,x(N)) is an element of Omega, for all i = 1, 2,...,k, (h(2)) there exists R is an element of R+\{0} such that R-N\ Omega subset of {(x1, x2,...,x(N)) is an element of R-N: Sigma(N)(j=k+1) x(j)(2) <= R-2} the existence of at least k + 1 solutions is proved.
2007
Pubblicato
Rilevanza internazionale
Articolo
Sì, ma tipo non specificato
Settore MAT/05 - ANALISI MATEMATICA
English
Con Impact Factor ISI
Nonlinear elliptic problems; Unbounded boundary; Unbounded domains
Cerami, G., Molle, R., Passaseo, D. (2007). Positive solutions of semilinear elliptic problems in unbounded domains with unbounded boundary. ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE, 24(1), 41-60 [10.1016/j.anihpc.2005.09.007].
Cerami, G; Molle, R; Passaseo, D
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/35074
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