Symmetry of positive solutions of elliptic equations with mixed boundary conditions in a super-spherical sector

2021 ◽  
Vol 60 (4) ◽  
Author(s):  
Ruofei Yao ◽  
Hongbin Chen ◽  
Changfeng Gui
Keyword(s):  
Boundary Conditions ◽  
Positive Solutions ◽  
Elliptic Equations ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions

Heterogeneous Elliptic BVPs with a Bifurcation-Continuation Parameter in the Nonlinear Mixed Boundary Conditions

2020 ◽  
Vol 20 (1) ◽  
pp. 31-51
Author(s):  
Santiago Cano-Casanova
Keyword(s):  
Boundary Conditions ◽  
Positive Solutions ◽  
Blow Up ◽  
Mixed Boundary ◽  
Elliptic Boundary ◽  
Global Bifurcation ◽  
Mixed Boundary Conditions ◽  
Elliptic Boundary Value ◽  
New Findings ◽  
Continuation Parameter

AbstractThis article ascertains the global structure of the diagram of positive solutions of a very general class of elliptic boundary value problems with spatial heterogeneities and nonlinear mixed boundary conditions, considering as bifurcation-continuation parameter a certain parameter γ that appears in the boundary conditions. In particular, in this work are obtained, in terms of such a parameter γ, the exact decay rate to zero and blow-up rate to infinity of the continuum of positive solutions of the problem, at the bifurcations from the trivial branch and from infinity. The new findings of this work complement, in some sense, those previously obtained for Robin linear boundary conditions by J. García-Melián, J. D. Rossi and J. C. Sabina de Lis in 2007. The main technical tools used to develop the mathematical analysis carried out in this paper are local and global bifurcation, continuation, comparison and monotonicity techniques and blow-up arguments.

Some Remarks on Elliptic Equations with Singular Potentials and Mixed Boundary Conditions

2004 ◽  
Vol 4 (4) ◽  
Author(s):  
Boumediene Abdellaoui ◽  
Eduardo Colorado ◽  
Ireneo Peral
Keyword(s):  
Boundary Conditions ◽  
Elliptic Equations ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Singular Potentials

AbstractWe study the problemswhere

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.

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