On a Class of Nonlinear Elliptic Problems with Neumann Boundary Conditions Growing Like a Power

1995 ◽  
Vol 14 (4) ◽  
pp. 853-868 ◽  
Author(s):  
Michel Chipot ◽  
F. Voirol
Keyword(s):  
Boundary Conditions ◽  
Elliptic Problems ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
Nonlinear Elliptic Problems ◽  
Nonlinear Elliptic

Infinitely Many Solutions for Mixed Elliptic Problems Involving the p−Laplacian

2015 ◽  
Vol 15 (4) ◽  
Author(s):  
Gabriele Bonanno ◽  
Giuseppina D’Aguí ◽  
Nikolaos S. Papageorgiou
Keyword(s):  
Boundary Conditions ◽  
Critical Point ◽  
Critical Point Theory ◽  
Elliptic Problems ◽  
Neumann Boundary ◽  
Point Theory ◽  
Laplacian Operator ◽  
Infinitely Many Solutions ◽  
Nonlinear Elliptic Problems ◽  
Nonlinear Elliptic

AbstractIn this paper the existence of infinitely many solutions for nonlinear elliptic problems involving the p-Laplacian operator with mixed Dirichlet-Neumann boundary conditions is established. The key assumption is a suitable oscillating behavior, either at infinity or at zero, of the nonlinearity. The approach is based on the critical point theory.

scholarly journals Existence of positive radial solutions for a class of nonlinear singular elliptic problems in annular domains

1992 ◽  
Vol 35 (3) ◽  
pp. 405-418 ◽  
Author(s):  
Zongming Guo
Keyword(s):  
Boundary Conditions ◽  
Degree Theory ◽  
Elliptic Problems ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
Radial Solutions ◽  
Positive Radial Solutions ◽  
Annular Domains ◽  
Radially Symmetric Solutions

We establish the existence of positive radially symmetric solutions of Δu+f(r,u,u′) = 0 in the domainR1<r<R0with a variety of Dirichlet and Neumann boundary conditions. The functionfis allowed to be singular when eitheru= 0 oru′ = 0. Our analysis is based on Leray-Schauder degree theory.

scholarly journals Nonresonance conditions on the potential for a nonlinear nonautonomous Neumann problem

2019 ◽  
Vol 38 (3) ◽  
pp. 79-96 ◽  
Author(s):  
Ahmed Sanhaji ◽  
A. Dakkak
Keyword(s):  
Boundary Conditions ◽  
Neumann Problem ◽  
Elliptic Problems ◽  
Neumann Boundary ◽  
Existence Results ◽  
Neumann Boundary Conditions ◽  
Laplacian Operator ◽  
First Eigenvalue ◽  
The First Eigenvalue

The aim of this paper is to establish the existence of the principal eigencurve of the p-Laplacian operator with the nonconstant weight subject to Neumann boundary conditions. We then study the nonresonce phenomena under the first eigenvalue and under the principal eigencurve, thus we obtain existence results for some nonautonomous Neumann elliptic problems involving the p-Laplacian operator.

scholarly journals Nonlinear elliptic equations involving the p-Laplacian with mixed Dirichlet-Neumann boundary conditions

2019 ◽  
Vol 39 (2) ◽  
pp. 159-174 ◽  
Author(s):  
Gabriele Bonanno ◽  
Giuseppina D'Aguì ◽  
Angela Sciammetta
Keyword(s):  
Boundary Conditions ◽  
Elliptic Equations ◽  
Mixed Boundary ◽  
Neumann Boundary ◽  
Nonlinear Elliptic Equations ◽  
Mixed Boundary Conditions ◽  
Neumann Boundary Conditions ◽  
Laplacian Operator ◽  
Differential Problem ◽  
Nonlinear Elliptic

In this paper, a nonlinear differential problem involving the \(p\)-Laplacian operator with mixed boundary conditions is investigated. In particular, the existence of three non-zero solutions is established by requiring suitable behavior on the nonlinearity. Concrete examples illustrate the abstract results.

scholarly journals Renormalized solutions for some nonlinear nonhomogeneous elliptic problems with Neumann boundary conditions and right hand side measure

2021 ◽  
Vol 39 (6) ◽  
pp. 81-103
Author(s):  
Elhoussine Azroul ◽  
Mohamed Badr Benboubker ◽  
Rachid Bouzyani ◽  
Houssam Chrayteh
Keyword(s):  
Boundary Conditions ◽  
Radon Measure ◽  
Elliptic Problems ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
Measure Data ◽  
Renormalized Solutions ◽  
Renormalized Solution ◽  
Nonhomogeneous Boundary ◽  
Nonhomogeneous Boundary Conditions

Our aim in this paper is to study the existence of renormalized solution for a class of nonlinear p(x)-Laplace problems with Neumann nonhomogeneous boundary conditions and diuse Radon measure data which does not charge the sets of zero p(.)-capacity

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