existence and multiplicity of nontrivial solutions for $p$-laplacian system with nonlinearities of concave-convex type and sign-changing weight functions
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this paper is concerned with the existence of multiple positive solutions for a quasilinear elliptic system involving concave-convex nonlinearities and sign-changing weight functions. with the help of the nehari manifold and palais-smale condition, we prove that the system has at least two nontrivial positive solutions, when the pair of parameters $(lambda,mu)$ belongs to a certain subset of $mathbb{r}^2$.
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Existence and multiplicity of nontrivial solutions for $p$-Laplacian system with nonlinearities of concave-convex type and sign-changing weight functions
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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 λ,μ varies and try to establish the existence of multiple positive solutions. c © 2007 Elsevier Ltd. All rights reserved.
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Journal title:
bulletin of the iranian mathematical societyجلد ۴۰، شماره ۵، صفحات ۱۳۰۱-۱۳۲۶
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