scholarly journals Multiple solutions for semilinear elliptic equations with Neumann boundary condition and jumping nonlinearities

2010 ◽  
Vol 371 (2) ◽  
pp. 682-690 ◽  
Author(s):  
Jing Zhang ◽  
Shujie Li ◽  
Yuwen Wang ◽  
Xiaoping Xue
Keyword(s):  
Boundary Condition ◽  
Elliptic Equations ◽  
Neumann Boundary Condition ◽  
Multiple Solutions ◽  
Neumann Boundary ◽  
Semilinear Elliptic Equations ◽  
Semilinear Elliptic ◽  
Jumping Nonlinearities

Multiple Solutions for a Class of Neumann Elliptic Problems on Compact Riemannian Manifolds with Boundary

2010 ◽  
Vol 53 (4) ◽  
pp. 674-683 ◽  
Author(s):  
Alexandru Kristály ◽  
Nikolaos S. Papageorgiou ◽  
Csaba Varga
Keyword(s):  
Boundary Condition ◽  
Riemannian Manifolds ◽  
Neumann Boundary Condition ◽  
Multiple Solutions ◽  
Compact Riemannian Manifold ◽  
Neumann Boundary ◽  
Manifolds With Boundary ◽  
Semilinear Elliptic Problem ◽  
Semilinear Elliptic ◽  
Manifold With Boundary

AbstractWe study a semilinear elliptic problem on a compact Riemannian manifold with boundary, subject to an inhomogeneous Neumann boundary condition. Under various hypotheses on the nonlinear terms, depending on their behaviour in the origin and infinity, we prove multiplicity of solutions by using variational arguments.

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.

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