Multiple solutions for semilinear elliptic equations in unbounded cylinder domains

Tsing-San Hsu

doi:10.1017/S0308210500003449

Abstract

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In this paper, we show that if b(x) ≥ b∞ > 0 in Ω̄ and there exist positive constants C, δ, R0 such that where x = (y, z) ∈ RN with y ∈ Rm, z ∈ Rn, N = m + n ≥ 3, m ≥ 2, n ≥ 1, 1 < p < (N + 2)/(N − 2), ω ⊆ Rm a bounded C1,1 domain and Ω = ω × Rn, then the Dirichlet problem −Δu + u = b(x)|u|p−1u in Ω has a solution that changes sign in Ω, in addition to a positive solution.

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Hsu, Tsing-San 2006. Existence of multiple positive solutions of subcritical semilinear elliptic problems in exterior strip domains. Nonlinear Analysis: Theory, Methods & Applications, Vol. 64, Issue. 6, p. 1203.

Hsu, Tsing-San 2006. Existence and bifurcation for some elliptic problems on exteriorstrip domains. International Journal of Mathematics and Mathematical Sciences, Vol. 2006, Issue. 1,

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Hsu, Tsing-San and Lin, Huei-Li 2007. Eigenvalue problems of nonhomogeneous semilinear elliptic equations in Esteban–Lions domains with holes. Journal of Mathematical Analysis and Applications, Vol. 330, Issue. 2, p. 1273.

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Multiple solutions for semilinear elliptic equations in unbounded cylinder domains

Abstract

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