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.

The Heat Equation for the -Neumann Problem, II

1988 ◽  
Vol 40 (2) ◽  
pp. 502-512 ◽  
Author(s):  
Richard Beals ◽  
Nancy K. Stanton
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Neumann Problem ◽  
Elliptic Boundary ◽  
Neumann Boundary ◽  
Hermitian Manifold ◽  
Neumann Boundary Conditions ◽  
Compact Manifolds ◽  
Elliptic Boundary Value ◽  
Image Position

Let Ω be a compact complex n + 1-dimensional Hermitian manifold with smooth boundary M. In [2] we proved the following.THEOREM 1. Suppose satisfies condition Z(q) with 0 ≦ q ≦ n. Let □p,q denote the -Laplacian on (p, q) forms onwhich satisfy the -Neumann boundary conditions. Then as t → 0;,(0.1)(If q = n + 1, the -Neumann boundary condition is the Dirichlet boundary condition and the corresponding result is classical.)Theorem 1 is a version for the -Neumann problem of results initiated by Minakshisundaram and Pleijel [8] for the Laplacian on compact manifolds and extended by McKean and Singer [7] to the Laplacian with Dirichlet or Neumann boundary conditions and by Greiner [5] and Seeley [9] to elliptic boundary value problems on compact manifolds with boundary. McKean and Singer go on to show that the coefficients in the trace expansion are integrals of local geometric invariants.

scholarly journals On the spectrum of one dimensional p-Laplacian for an eigenvalue problem with Neumann boundary conditions

2013 ◽  
Vol 33 (1) ◽  
pp. 9
Author(s):  
Ahmed Dakkak ◽  
Siham El Habib ◽  
Najib Tsouli
Keyword(s):  
Eigenvalue Problem ◽  
Boundary Conditions ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
Laplacian Operator ◽  
Strict Monotonicity ◽  
Indefinite Weight ◽  
One Dimensional ◽  
Weight One

This work deals with an indefinite weight one dimensional eigenvalue problem of the p-Laplacian operator subject to Neumann boundary conditions. We are interested in some properties of the spectrum like simplicity, monotonicity and strict monotonicity with respect to the weight. We also aim the study of zeros points of eigenfunctions.

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 Sharp estimates for the first p-Laplacian eigenvalue and for the p-torsional rigidity on convex sets with holes

2020 ◽  
Vol 26 ◽  
pp. 111 ◽  
Author(s):  
Gloria Paoli ◽  
Gianpaolo Piscitelli ◽  
Leonardo Trani
Keyword(s):  
Boundary Conditions ◽  
Convex Sets ◽  
Torsional Rigidity ◽  
Neumann Boundary ◽  
Robin Boundary Conditions ◽  
First Eigenvalue ◽  
Laplacian Eigenvalue ◽  
Sharp Estimates ◽  
The First Eigenvalue ◽  
Robin Boundary

We study, in dimension n ≥ 2, the eigenvalue problem and the torsional rigidity for the p-Laplacian on convex sets with holes, with external Robin boundary conditions and internal Neumann boundary conditions. We prove that the annulus maximizes the first eigenvalue and minimizes the torsional rigidity when the measure and the external perimeter are fixed.

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 Behavior of the -Laplacian on Thin Domains

2013 ◽  
Vol 2013 ◽  
pp. 1-4 ◽  
Author(s):  
Ricardo P. Silva
Keyword(s):  
Boundary Conditions ◽  
Elliptic Equations ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
Laplacian Operator ◽  
Thin Domains ◽  
Limiting Behavior

We give the characterization of the limiting behavior of solutions of elliptic equations driven by the -Laplacian operator with Neumann boundary conditions posed in a family of thin domains.

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