POSITIVE SOLUTIONS OF NONLINEAR ELLIPTIC EQUATIONS WITH MIXED BOUNDARY CONDITIONS

1992 ◽  
Vol 12 (3) ◽  
pp. 292-303
Author(s):  
Ruying Xue
Keyword(s):  
Boundary Conditions ◽  
Positive Solutions ◽  
Elliptic Equations ◽  
Mixed Boundary ◽  
Nonlinear Elliptic Equations ◽  
Mixed Boundary Conditions ◽  
Nonlinear Elliptic

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 Positive Solutions of Nonlinear Elliptic Equations with Nonlinear Boundary Conditions

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Hua Luo
Keyword(s):  
Boundary Conditions ◽  
Positive Solutions ◽  
Elliptic Equations ◽  
Nonlinear Boundary ◽  
Eigenvalue Problems ◽  
Nonlinear Elliptic Equations ◽  
Nonlinear Boundary Conditions ◽  
Nonlinear Elliptic ◽  
Elliptic Eigenvalue Problems ◽  
Bifurcation From Interval

This paper discusses bifurcation from interval for the elliptic eigenvalue problems with nonlinear boundary conditions and studies the behavior of the bifurcation components.

Existence of two solutions of nonlinear elliptic equations with critical Sobolev exponents and mixed boundary conditions

1996 ◽  
Vol 126 (1) ◽  
pp. 47-75 ◽  
Author(s):  
Feimin Huang
Keyword(s):  
Elliptic Equations ◽  
Mixed Boundary ◽  
Nonlinear Elliptic Equations ◽  
Mixed Boundary Conditions ◽  
Sobolev Embedding ◽  
Lipschitz Continuous ◽  
Nonlinear Elliptic ◽  
Critical Sobolev Exponents ◽  
Image Position ◽  
Continuous Boundary

Let Ω be a bounded domain in Rn(n ≧ 3) with Lipschitz-continuous boundary, ∂Ω = Γ0∪Γ1. In this paper we consider the following problem:where φ ∈ L2 (Γ1), φ ≢ 0 on Γ1 and γ is the unit outward normal and p = 2n/(n − 2) = 2* is the critical exponent for the Sobolev embedding . We prove that for φ ∈ L2(Γ1) satisfying suitable conditions, the problem admits two solutions.

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