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On the existence and multiplicity of positive solutions for some indefinite nonlinear eigenvalue problem. (English) Zbl 1129.35054

Summary: This paper is concerned with the existence, uniqueness and/or multiplicity, and stability of positive solutions of an indefinite weight elliptic problem with concave or convex nonlinearity. We use mainly bifurcation methods to obtain our results.

MSC:

35P30 Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs
35B35 Stability in context of PDEs
35J60 Nonlinear elliptic equations
47J10 Nonlinear spectral theory, nonlinear eigenvalue problems
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