Exact multiplicity results for a p-Laplacian positone problem with concave-convex-concave nonlinearities

Date

2004-05-20

Authors

Addou, Idris
Wang, Shin-Hwa

Journal Title

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Volume Title

Publisher

Southwest Texas State University, Department of Mathematics

Abstract

We study the exact number of positive solutions of a two-point Dirichlet boundary-value problem involving the p-Laplacian operator. We consider the case p = 2 and the case p > 1, when the nonlinearity ƒ satisfies ƒ(0) > 0 (positone) and has three distinct simple positive zeros and such that ƒ'' changes sign exactly twice on (0, ∞). Note that we may allow ƒ'' to change sign more than twice on (0, ∞). We also present some interesting examples.

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Keywords

Exact multiplicity result, p-Laplacian, Positone problem, Bifurcation, Concave-convex-concave nonlinearity, Positive solutions, Dead core solution, Time map

Citation

Addou, I., & Wang, S. H. (2004). Exact multiplicity results for a p-Laplacian positone problem with concave-convex-concave nonlinearities. <i>Electronic Journal of Differential Equations, 2004</i>(72), pp. 1-25.

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Attribution 4.0 International

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