The monotone method for periodic differential equations with the non well-ordered upper and lower solutions

Authors:
Aijun Yang;Weigao Ge
Affiliations:
Department of Applied Mathematics, Beijing Institute of Technology, Beijing, 100081, PR China;Department of Applied Mathematics, Beijing Institute of Technology, Beijing, 100081, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

Citing 3
Cited 0

Monotone method for the Neumann problem with lower and upper solutions in the reverse order

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Monotone method for singular Neumann problem

Nonlinear Analysis: Theory, Methods & Applications
Boundary value problems involving upper and lower solutions in reverse order

Journal of Computational and Applied Mathematics

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Abstract

In this paper, we consider the following periodic problem: x^''(t)=g(t,x(t),x^'(t)),a.e. t@?(a,b),x(a)=x(b),x^'(a)=x^'(b). The unique solution is obtained by constructing an auxiliary periodic system with bounded solutions and proving these bounds to be equal, in which case they are the expected unique solution.