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Positive mountain pass solutions for a semilinear elliptic equation with a sign-changing weight function

✍ Scribed by G.A. Afrouzi; K.J. Brown

Publisher
Elsevier Science
Year
2006
Tongue
English
Weight
121 KB
Volume
64
Category
Article
ISSN
0362-546X

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✦ Synopsis

We use the mountain pass theorem to study the existence and multiplicity of positive solutions of the generalisation of the well-known logistic equation -u = g(x)u(x)(1 -u(x)) with Dirichlet boundary conditions to the case where g changes sign.

πŸ“œ SIMILAR VOLUMES

Existence of multiple positive solutions
Existence of multiple positive solutions for a -Laplacian system with sign-changing weight functions
✍ Guoying Yang; Mingxin Wang πŸ“‚ Article πŸ“… 2008 πŸ› Elsevier Science 🌐 English βš– 322 KB

A p-Laplacian system with Dirichlet boundary conditions is investigated. By analysis of the relationship between the Nehari manifold and fibering maps, we will show how the Nehari manifold changes as Ξ», Β΅ varies and try to establish the existence of multiple positive solutions.

Blow-Up of Solutions with Sign Changes f
Blow-Up of Solutions with Sign Changes for a Semilinear Diffusion Equation
✍ Noriko Mizoguchi; Eiji Yanagida πŸ“‚ Article πŸ“… 1996 πŸ› Elsevier Science 🌐 English βš– 117 KB

0 with the Dirichlet, Neumann, or periodic boundary condition. Here ) 0 is a Ε½ . parameter, and f is an odd function of u satisfying f Ј 0 ) 0 and some convexity Ε½ . w x condition. Let z U be the number of times of sign changes for U g C 0, 1 . It is Γ„ 4 shown that there exists an increasing sequenc