scholarly journals Nonlinear Neumann Boundary Conditions for Quasilinear Degenerate Elliptic Equations and Applications

1999 ◽  
Vol 154 (1) ◽  
pp. 191-224 ◽  
Author(s):  
Guy Barles
Keyword(s):  
Boundary Conditions ◽  
Elliptic Equations ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
Degenerate Elliptic Equations ◽  
Degenerate Elliptic ◽  
Nonlinear Neumann Boundary Conditions

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.

Solutions for the microsensor thermistor equations in the small bias case

1993 ◽  
Vol 123 (6) ◽  
pp. 987-999 ◽  
Author(s):  
W. Allegretto ◽  
H. Xie
Keyword(s):  
Banach Space ◽  
Boundary Conditions ◽  
Implicit Function Theorem ◽  
Elliptic Equations ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
Implicit Function ◽  
Applied Bias

SynopsisThe behaviour of a microsensor thermistor is described by a system of nonlinear coupled elliptic equations subject to mixed Dirichlet-Neumann boundary conditions, to be solved on different domains. We employ the Implicit Function Theorem in Banach space to show that the system has a solution for small applied bias. It does not appear that earlier approaches for similar thermistor problems can be employed in this physically important situation. The fact that the problem is cast in a subset of R3 is significant in our presentation.

scholarly journals Multiple solutions for a class of bi-nonlocal problems with nonlinear Neumann boundary conditions

2022 ◽  
Vol 40 ◽  
pp. 1-11
Author(s):  
Ghasem A. Afrouzi ◽  
Z. Naghizadeh ◽  
Nguyen Thanh Chung
Keyword(s):  
Boundary Conditions ◽  
Variational Methods ◽  
Weak Solutions ◽  
Multiple Solutions ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
Nonlocal Problems ◽  
Mapping Theory ◽  
Nonlinear Neumann Boundary Conditions

In this paper, we are interested in a class of bi-nonlocal problems with nonlinear Neumann boundary conditions and sublinear terms at infinity. Using $(S_+)$ mapping theory and variational methods, we establish the existence of at least two non-trivial weak solutions for the problem provied that the parameters are large enough. Our result complements and improves some previous ones for the superlinear case when the Ambrosetti-Rabinowitz type conditions are imposed on the nonlinearities.

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