2006•International Mathematical ForumOpen access
On the study of existence and nonexistence of positive solutions for a superlinear Dirichlet problem
G. A. Afrouzi, S. Mahdavi, Z. Naghizadeh
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Abstract
We study the existence of positive solution for the equation −Δu = λ(u + u 2 + u 3 ) for x ∈ Ω whit Dirichlet boundary condition. And show that for every λ<λ 1, where λ1 is the first eigenvalue of −Δu = λu in Ω with the Dirichlet boundary condition, the equation has positive solution while no positive solution exists for λ ≥ λ1. Mathematics Subject Classification: 35B30, 35J20, 35J25