Existence of periodic solutions of higher-order differential equations

Authors:
Fu-Hsiang Wong;Shang-Wen Lin;Wei-Cheng Lian;Shiueh-Ling Yu
Affiliations:
-;-;-;-
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2005

Citing 1
Cited 3

Existence of positive solutions for non-positive higher-order BVPs

Journal of Computational and Applied Mathematics - Special issue: positive solutions of nonlinear problems

Existence of positive solutions for n+2 order p-Laplacian BVP

Computers & Mathematics with Applications
Existence of positive solutions for various boundary value problems

Computers & Mathematics with Applications
Existence of positive solutions for an (n+2)-order nonlinear BVP

Computers & Mathematics with Applications

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Abstract

We established some sufficient conditions for the existence of solutions of high-order periodic boundary value problem for n = 2 (E)u^(^n^)(t)+D(t,u(t),...,u^(^n^-^2^)(t))u^(^n^-^1^)(t)+g(t,u(t),...,u^(^n^-^2^)(t))=h(t),fort@?[0,T],(BC){u^(^i^)(0)=0,i=0,1,2,...,n-3,(BVP)u^(^n^-^2^)(0)=u^(^n^-^2^)(T),u^(^n^-^1^)(0)=u^(^n^-^1^)(T), where h @e L^1(0,T), D @e C([0,T]x R^n^-^1,R), and g:[0,T] x R^n^-^1 - R be a Caratheodory function, T-periodic in the first variable.