scholarly journals The existence and uniqueness of the global solution for the viscoelastic-plate equation under nonlinear boundary conditions

2008 ◽  
Vol 57 (11) ◽  
pp. 6741
Author(s):  
Wang Dan-Xia ◽  
Zhang Jian-Wen ◽  
Wu Run-Heng
Keyword(s):  
Boundary Conditions ◽  
Global Solution ◽  
Existence And Uniqueness ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Conditions ◽  
Viscoelastic Plate ◽  
Plate Equation

scholarly journals TWO INITIAL-BOUNDARY VALUE PROBLEMS WITH NONLINEAL BOUNDARY CONDITIONS FOR ONE-DIMENSION HYPERBOLIC EQUATION

2017 ◽  
Vol 17 (2) ◽  
pp. 46-56
Author(s):  
L.S. Pulkina ◽  
M.V. Strigun
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Existence And Uniqueness ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Initial Boundary ◽  
Nonlinear Boundary Conditions ◽  
One Dimension ◽  
Initial Boundary Value Problems ◽  
Initial Boundary Value

In this paper, the initial-boundary value problems for hyperbolic equationwith nonlinear boundary conditions are considered. Existence and uniqueness ofgeneralized solution are proved.

scholarly journals Existence and Uniqueness of the Solutions for Fractional Differential Equations with Nonlinear Boundary Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Xiping Liu ◽  
Fanfan Li ◽  
Mei Jia ◽  
Ertao Zhi
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Nonlinear Boundary Conditions ◽  
Iterative Sequence ◽  
Fractional Differential

We study the existence and uniqueness of the solutions for the boundary value problem of fractional differential equations with nonlinear boundary conditions. By using the upper and lower solutions method in reverse order and monotone iterative techniques, we obtain the sufficient conditions of both the existence of the maximal and minimal solutions between an upper solution and a lower solution and the uniqueness of the solutions for the boundary value problem and present the iterative sequence for calculating the approximate analytical solutions of the boundary value problem and the error estimate. An example is also given to illustrate the main results.

scholarly journals THE COMPETITION BETWEEN INCOMING AND OUTGOING FLUXES IN AN ELLIPTIC PROBLEM

2007 ◽  
Vol 09 (06) ◽  
pp. 781-810
Author(s):  
JORGE GARCÍA-MELIÁN ◽  
JULIO D. ROSSI ◽  
ANTONIO SUÁREZ
Keyword(s):  
Elliptic Equation ◽  
Boundary Conditions ◽  
Bifurcation Diagram ◽  
Elliptic Problem ◽  
Existence And Uniqueness ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Conditions ◽  
Smooth Bounded Domain ◽  
Comparison Arguments ◽  
Outward Unit

In this work, we consider existence and uniqueness of positive solutions to the elliptic equation -Δu = λu in Ω, with the nonlinear boundary conditions [Formula: see text] on Γ1, [Formula: see text] on Γ2, where Ω is a smooth bounded domain, ∂Ω = Γ1 ∪ Γ2, [Formula: see text], ν is the outward unit normal, p, q > 0 and λ is a real parameter. We obtain a complete picture of the bifurcation diagram of the problem, depending on the values of p, q and the parameter λ. Our proofs are based on different techniques: variational arguments, bifurcation techniques or comparison arguments, depending on the range of parameters considered.

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