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Topological Methods in Nonlinear Analysis

Existence of multiple solutions for a quasilinear elliptic problem
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Existence of multiple solutions for a quasilinear elliptic problem

Authors

  • Jorge Cossio
  • Sigifredo Herrón
  • Carlos Vélez

Keywords

Quasilinear elliptic equations, bifurcation theory, multiplicity of solutions

Abstract

In this paper we prove the existence of multiple solutions for a quasilinear elliptic boundary value problem, when the $p$-derivative at zero and the $p$-derivative at infinity of the nonlinearity are greater than the first eigenvalue of the $p$-Laplace operator. Our proof uses bifurcation from infinity and bifurcation from zero to prove the existence of unbounded branches of positive solutions (resp. of negative solutions). We show the existence of multiple solutions and we provide qualitative properties of these solutions.

References

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Published

2017-10-01

How to Cite

1.
COSSIO, Jorge, HERRÓN, Sigifredo and VÉLEZ, Carlos. Existence of multiple solutions for a quasilinear elliptic problem. Topological Methods in Nonlinear Analysis. Online. 1 October 2017. Vol. 50, no. 2, pp. 531 - 551. [Accessed 3 July 2025].
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