The existence of positive solutions for an elliptic boundary value problem | Zendy

G. A. Afrouzi | Zendy

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The existence of positive solutions for an elliptic boundary value problem

Author(s) -

G. A. Afrouzi

Publication year - 2005

Publication title -

international journal of mathematics and mathematical sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.21

H-Index - 39

eISSN - 1687-0425

pISSN - 0161-1712

DOI - 10.1155/ijmms.2005.2005

Subject(s) - mathematics , boundary value problem , dirichlet eigenvalue , dirichlet boundary condition , dirichlet problem , lemma (botany) , mathematical analysis , elliptic boundary value problem , boundary values , eigenvalues and eigenvectors , mountain pass , dirichlet distribution , elliptic curve , boundary (topology) , dirichlet's principle , pure mathematics , mixed boundary condition , physics , ecology , poaceae , quantum mechanics , biology

By using the mountain pass lemma, we study the existence ofpositive solutions for the equation −Δu(x)=λ(u|u|+u)(x) for x∈Ω together with Dirichletboundary conditions and show that for every λ<λ1,where λ1 is the first eigenvalue of −Δu=λu in Ω with the Dirichlet boundary conditions, the equationhas a positive solution while no positive solution exists forλ≥λ1

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