Nonnegative Solutions of a Fredholm Type Integral Equation with Applications to Boundary Value Problems

Authors:
Rui A. Ferreira
Affiliations:
Department of Mathematics, Lusophone University of Humanities and Technologies, Lisbon, Portugal 1749-024 and Center for Research and Development in Mathematics and Applications, University of Ave ...
Venue:
Acta Applicandae Mathematicae: an international survey journal on applying mathematics and mathematical applications
Year:
2012

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Abstract

One studies the existence of nonnegative solutions of the integral equation $$u(t)=h(t)+\int_a^bG(t,s)f(s,u(s),u'(s))ds,\quad t\in[a,b],$$ under some suitable conditions on the functions f, G and h. The results obtained are then applied to some nonlinear boundary value problems.