scholarly journals Semilinear elliptic problems with mixed Dirichlet–Neumann boundary conditions

2003 ◽  
Vol 199 (2) ◽  
pp. 468-507 ◽  
Author(s):  
E. Colorado ◽  
I. Peral
Keyword(s):  
Boundary Conditions ◽  
Elliptic Problems ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
Semilinear Elliptic ◽  
Semilinear Elliptic Problems

On the Number of Solutions to Semilinear Boundary Value Problems

2004 ◽  
Vol 4 (3) ◽  
Author(s):  
Markus Kunze ◽  
Rafael Ortega
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Upper Bound ◽  
Dirichlet Boundary ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
Dirichlet Boundary Conditions ◽  
Number Of Solutions ◽  
Semilinear Elliptic ◽  
Semilinear Elliptic Problems

AbstractWe consider semilinear elliptic problems of the form Δu + g(u) = f(x) with Neumann boundary conditions or Δu+λ1u+g(u) = f(x) with Dirichlet boundary conditions, and we derive conditions on g and f under which an upper bound on the number of solutions can be obtained.

Symmetry properties of positive solutions of elliptic equations in an infinite sectorial cone

1992 ◽  
Vol 122 (1-2) ◽  
pp. 137-160
Author(s):  
Chie-Ping Chu ◽  
Hwai-Chiuan Wang
Keyword(s):  
Boundary Conditions ◽  
Positive Solution ◽  
Positive Solutions ◽  
Elliptic Equations ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
Semilinear Elliptic Equations ◽  
Spherically Symmetric ◽  
Semilinear Elliptic ◽  
Symmetry Properties

SynopsisWe prove symmetry properties of positive solutions of semilinear elliptic equations Δu + f(u) = 0 with Neumann boundary conditions in an infinite sectorial cone. We establish that any positive solution u of such equations in an infinite sectorial cone ∑α in ℝ3 is spherically symmetric if the amplitude α of ∑α is not greater than π.

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.

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