### Multiple solutions to a Dirichlet eigenvalue problem with $p$-Laplacian

#### Abstract

The existence of a greatest negative, a smallest positive, and

a nodal weak solution to a homogeneous Dirichlet problem with

$p$-Laplacian and reaction term depending on a positive

parameter is investigated via variational as well as topological

methods, besides truncation techniques.

a nodal weak solution to a homogeneous Dirichlet problem with

$p$-Laplacian and reaction term depending on a positive

parameter is investigated via variational as well as topological

methods, besides truncation techniques.

#### Keywords

Dirichlet eigenvalue problem; p-Laplacian; constant-sign solutions; nodal solutions

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