scholarly journals First-Order Boundary Value Problem with Nonlinear Boundary Condition on Time Scales

2011 ◽  
Vol 2011 ◽  
pp. 1-8 ◽  
Author(s):  
Ya-Hong Zhao
Keyword(s):  
Boundary Condition ◽  
Boundary Value Problem ◽  
Dynamic Equation ◽  
Iteration Method ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Condition ◽  
Iterative Schemes ◽  
First Order ◽  
Monotone Iteration ◽  
Existence Of Positive Solutions

This work is concerned with the following first-order dynamic equation on time scale, xΔ(t)+p(t)x(σ(t))=f(t,x(t)),  t∈[0,T]𝕋with the nonlinear boundary conditionx(0)=g(x(σ(T))). By applying monotone iteration method, we not only obtain the existence of positive solutions, but also establish iterative schemes for approximating the solutions.

scholarly journals On a first-order semipositone boundary value problem on a time scale

2014 ◽  
Vol 8 (2) ◽  
pp. 269-287
Author(s):  
Christopher Goodrich
Keyword(s):  
Boundary Condition ◽  
Boundary Value Problem ◽  
Positive Solution ◽  
Difference Equations ◽  
Dynamic Equation ◽  
Time Scale ◽  
Boundary Value ◽  
First Order ◽  
General Time

We consider the existence of a positive solution to the first-order dynamic equation y?(t)+p(t)y?(t) = ?f (t, y?(t)), t?(a, b)T, subject to the boundary condition y(a) = y(b) + ?T1,T2 F(s, y(s)) ?s for ?1,?2 ? [a,b]T. In this setting, we allow f to take negative values for some (t; y). Our results generalize some recent results for this class of problems, and because we treat the problem on a general time scale T we provide new results for this problem in the case of differential, difference, and q-difference equations. We also provide some discussion of the applicability of our results.

A shock problem involving a nonlinear viscoelastic bar associated with a nonlinear boundary condition

2008 ◽  
Vol 41 (1) ◽  
Author(s):  
Nguyen Thanh Long ◽  
Vo Giang Giai ◽  
Le Xuan Truong
Keyword(s):  
Boundary Condition ◽  
Wave Equation ◽  
Boundary Value Problem ◽  
Nonlinear Wave Equation ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Condition ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Nonlinear Viscoelastic ◽  
Initial Boundary Value

AbstractWe study the initial-boundary value problem for a nonlinear wave equation given by

scholarly journals First order differential systems with a nonlinear boundary condition via the method of solution-regions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Marlène Frigon ◽  
Marcos Tella ◽  
F. Adrián F. Tojo
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Condition ◽  
Nonlinear Boundary Conditions ◽  
Linear Case ◽  
Differential Systems ◽  
First Order ◽  
Method Of Solution

AbstractIn this article we extend the known theory of solution regions to encompass nonlinear boundary conditions. We both provide results for new boundary conditions and recover some known results for the linear case.

Sign in / Sign up

Export Citation Format

Share Document