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Existence and Multiplicity of Solutions for Noncoercive Neumann Problems with p-Laplacian

100%

Gasiński L. , Papageorgiou N. S.

Schedae Informaticae

2012

tom Vol. 21

27--40

We consider a nonlinear Neumann elliptic equation driven by the p-Laplacian and a Caratheodory perturbation. The energy functional of the problem need not be coercive. Using variational methods we prove an existence theorem and a multiplicity theorem, producing two nontrivial smooth solutions. Our formulation incorporates strongly resonant equations.

Existence and multiplicity of solutions for a nonhomogeneous Neumann boundary problem

100%

Klimczak L.

Opuscula Mathematica

2015

tom Vol. 35, no. 6

889--905

We consider a nonlinear Neumann elliptic equation driven by a p-Laplacian-type operator which is not homogeneous in general. For such an equation the energy functional does not need to be coercive, and we use suitable variational methods to show that the problem has at least two distinct, nontrivial smooth solutions. Our formulation incorporates strongly resonant equations.

On the existence of five nontrivial solutions for resonant problems with p-Laplacian

75%

Gasiński L. , Papageorgiou N.

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

2010

tom 30

nr 2

169-189

In this paper we study a nonlinear Dirichlet elliptic differential equation driven by the p-Laplacian and with a nonsmooth potential. The hypotheses on the nonsmooth potential allow resonance with respect to the principal eigenvalue λ₁ > 0 of $(-Δₚ,W₀^{1,p}(Z))$. We prove the existence of five nontrivial smooth solutions, two positive, two negative and the fifth nodal.