Positive solvability of systems of nonlinear Hammerstein integral equations

Abstract

The paper deals with the existence of positive continuous solutions to systems of nonlinear Hammerstein integral equations. The main tool used in the proofs is fixed point index theory in a cone. The results obtained here are essentially different from existing ones in the literature.  2005 Elsevier Inc. All rights reserved.

Positive solutions of a second-order integral boundary value problem

“…This proves (25). Now taking ξ 3 > 0 sufficiently small so that r(N) < 1, with N being defined by (20), we see from (H3) and (H5) that there is r > 0 such that (H2) holds.…”

“…[25] Let E be a real Banach space and W a total cone[1] of E. Suppose B : P → P is a bounded linear operator (therefore, B can be uniquely extended to a bounded linear operator on P − P = E, and the extended operator is denoted by B again) with r(B) < 1. If w 0 ∈ E, w ∈ E satisfies w w 0 + Bw, then w (I − B) −1 w 0 , where (I − B) −1 is the inverse operator of I − B.…”

Positive solutions for a system of nonlocal fractional boundary value problems

“…For other papers in which there are studied Hammerstein integrals systems, we refer the reader to [17], [21], [26].…”

Existence of positive solutions for a system of generalized Lidstone problems

“…For more details, see, for instance, [21][22][23][24]. Recently, in [25], using fixed point theory, Infante et al considered the existence and multiplicity of positive solutions for a system of perturbed Hammerstein integral equations, with the main results applied to a wide class of boundary value problems.…”