Analyzing and visualizing a discretized semilinear elliptic problem with Neumann boundary conditions

2002 ◽  
Vol 18 (3) ◽  
pp. 261-279 ◽  
Author(s):  
Tsung-Min Hwang ◽  
Weichung Wang
Keyword(s):  
Boundary Conditions ◽  
Elliptic Problem ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
Semilinear Elliptic Problem ◽  
Semilinear Elliptic

Solution branches of a semilinear elliptic problem at corank-2 bifurcation points with Neumann boundary conditions

1993 ◽  
Vol 123 (3) ◽  
pp. 479-495 ◽  
Author(s):  
Mei Zhen
Keyword(s):  
Boundary Conditions ◽  
Elliptic Problem ◽  
Bifurcation Point ◽  
Continuation Method ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
Bifurcation Points ◽  
Semilinear Elliptic Problem ◽  
Semilinear Elliptic ◽  
Branch Switching

SynopsisSolution branches of a semilinear elliptic problem with Neumann boundary conditions are studied at its corank-2 bifurcation points. It is shown that generally there are exactly four different nontrivial solution branches passing through a corank-2 bifurcation point. The bifurcating solution branches are parametrised via a nonsingular enlarged problem. Branch switching at bifurcation points is incorporated with a continuation method.

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.

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.

scholarly journals On the existence of nontrivial solutions for a fourth-order semilinear elliptic problem

2005 ◽  
Vol 2005 (6) ◽  
pp. 673-683
Author(s):  
Aixia Qian ◽  
Shujie Li
Keyword(s):  
Boundary Conditions ◽  
Nontrivial Solution ◽  
Fourth Order ◽  
Elliptic Problem ◽  
Nontrivial Solutions ◽  
Navier Boundary Conditions ◽  
Minimax Theory ◽  
Semilinear Elliptic Problem ◽  
Semilinear Elliptic

By means of Minimax theory, we study the existence of one nontrivial solution and multiple nontrivial solutions for a fourth-order semilinear elliptic problem with Navier boundary conditions.

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