ON THE POSITIVE SOLUTIONS OF THE LOGISTIC WEIGHTED ELLIPTIC BVP WITH SUBLINEAR MIXED BOUNDARY CONDITIONS

2005 ◽  
Author(s):  
S. CANO-CASANOVA
Keyword(s):  
Boundary Conditions ◽  
Positive Solutions ◽  
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.

scholarly journals Iterative positive solutions to a coupled fractional differential system with the multistrip and multipoint mixed boundary conditions

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Xiaodi Zhao ◽  
Yuehan Liu ◽  
Huihui Pang
Keyword(s):  
Boundary Conditions ◽  
Positive Solutions ◽  
Mixed Boundary ◽  
Coupled System ◽  
Mixed Boundary Conditions ◽  
Monotone Iterative Technique ◽  
Monotone Iterative ◽  
Fractional Differential System ◽  
Fractional Differential ◽  
Derivatives Of

Abstract Using the monotone iterative technique, we investigate the existence of iterative positive solutions to a coupled system of fractional differential equations supplemented with multistrip and multipoint mixed boundary conditions. It is worth mentioning that the nonlinear terms of the system depend on the lower fractional-order derivatives of the unknown functions and the boundary conditions involve the combination of the multistrip fractional integral and the multipoint value of the unknown functions in $[0,1]$ [ 0 , 1 ] .

scholarly journals EXISTENCE AND UNIQUENESS OF POSITIVE SOLUTIONS TO ELLIPTIC PROBLEMS WITH SUBLINEAR MIXED BOUNDARY CONDITIONS

2009 ◽  
Vol 11 (04) ◽  
pp. 585-613 ◽  
Author(s):  
JORGE GARCÍA-MELIÁN ◽  
JULIO D. ROSSI ◽  
JOSÉ C. SABINA DE LIS
Keyword(s):  
Boundary Conditions ◽  
Positive Solutions ◽  
Nonlinear Boundary ◽  
Mixed Boundary ◽  
Elliptic Problems ◽  
Mixed Boundary Conditions ◽  
Nonlinear Boundary Conditions ◽  
Semilinear Elliptic ◽  
Semilinear Elliptic Problems ◽  
Outward Unit

In this work, we consider a class of semilinear elliptic problems with nonlinear boundary conditions of mixed type. Under some monotonicity properties of the nonlinearities involved, we show that positive solutions are unique, and that their existence is characterized by the sign of some associated eigenvalues. One of the most important contributions of this work relies on the fact that we deal with boundary conditions of the form ∂u/∂ν = g(x,u) on Γ and u = 0 on Γ', where ν is the outward unit normal to Γ while Γ,Γ' are open, Γ ∩ Γ' = ∅, [Formula: see text], but [Formula: see text] need not be disjoint.

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