We consider a semilinear elliptic partial differential equation, depending on two positive parameters λ and μ, coupled with homogeneous Dirichlet boundary conditions. Assuming only one-sided growth conditions on the nonlinearities involved, we prove the existence of at least three weak solutions for λ and μ lying in convenient intervals. We employ techniques of nonsmooth analysis introduced by Degiovanni and Zani, and a theorem of Ricceri for multiplicity of local minimizers.
Three solutions for a Dirichlet problem with one-sided growth conditions on the nonlinearities
IANNIZZOTTO, ANTONIO
2013-01-01
Abstract
We consider a semilinear elliptic partial differential equation, depending on two positive parameters λ and μ, coupled with homogeneous Dirichlet boundary conditions. Assuming only one-sided growth conditions on the nonlinearities involved, we prove the existence of at least three weak solutions for λ and μ lying in convenient intervals. We employ techniques of nonsmooth analysis introduced by Degiovanni and Zani, and a theorem of Ricceri for multiplicity of local minimizers.
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