Positive Periodic Solution for Second-Order Singular Semipositone Differential Equations

Abstract

We study the existence of a positive periodic solution for second-order singular semipositone differential equation by a nonlinear alternative principle of Leray-Schauder. Truncation plays an important role in the analysis of the uniform positive lower bound for all the solutions of the equation. Recent results in the literature (Chu et al., 2010) are generalized.

On the existence of a solution of a second‐order singular initial value problem

“…We try to find the conditions for p ( t ) and q ( t , x ( t )) such that provides the existence of the solution. For the existence of the solutions of a second‐order initial/boundary problems with different type of singularities, see, for example, …”

“…We try to find the conditions for p.t/ and q.t, x.t// such that provides the existence of the solution. For the existence of the solutions of a second-order initial/boundary problems with different type of singularities, see, for example, [5,[19][20][21][22][23][24][25][26][27][28][29][30][31][32] (a) for each t 2 .0, 1, q.t, ./ is continuous on OE˛,ˇ; (b) for each x 2 OE˛,ˇ, q.., x/ is measurable on OE0, 1; (c) jq.t, x/j Ä K Then, a solution to the initial value problem (2) exists.…”