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Positive solutions of semi-positone Hammerstein integral equations and applications. (English) Zbl 1134.45005

The author considers the following Hammerstein integral equation:

y(t)= 0 1 k(t,s)g(s)f(s,y(s))ds,t[0,1],(1)

where f:[0,1]× + is continuous, and such that f>-η for some η>0; the kernel k:[0,1]×[0,1] + is continuous; g:[0,1] + is measurable. The author uses the fixed-point index theory to prove the existence of one or several positive solutions for problem (1). Furthermore, he applies the obtained results to some nth order ordinary differential equations with boundary conditions.

MSC:
45G10Nonsingular nonlinear integral equations
47H30Particular nonlinear operators
45M20Positive solutions of integral equations
34B15Nonlinear boundary value problems for ODE