The existence of multiple positive solutions to boundary value problems of nonlinear delay differential equations with countably many singularities on infinite interval

Authors:
Yuming Wei;Patricia J. Y. Wong;Weigao Ge
Affiliations:
School of Mathematical Science, Guangxi Normal University, Guilin, 541004, China and Department of Mathematics, Beijing Institute of Technology, Beijing 100081, China;School of Electrical and Electronic Engineering, Nanyang Technological University, 639798, Singapore;Department of Mathematics, Beijing Institute of Technology, Beijing 100081, China
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

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Abstract

In this paper, we consider the existence of countably many positive solutions to a boundary value problem of a nonlinear delay differential equation with countably many singularities on infinite interval (@f(x^'(t)))^'+a(t)f(t,x(t),x"t)=0,0~x^'(t)=0, where @f:R-R is an increasing homeomorphism and a positive homomorphism with @f(0)=0,x"t is a function in C([-r,0],R) defined by x"t(@s)=x(t+@s) for -r@?@s@?0, and @x@?C([-r,0],R). By using the fixed-point index theory and a new fixed-point theorem in a cone, we provide sufficient conditions for the existence of multiple positive solutions to the above boundary value problem. The conclusions in this paper essentially extend and improve the known results.