Boundary Value Problems · 2014 · 27 citations · 22 references
Natural SciencesMathematicsApplied MechanicsDifferential EquationsDynamical SystemsExistence TheoremsExistence TheoryFixed Point TheoryFixed PointsInitial Value ProblemsIntegral EquationsExistence Of Fixed PointsFixed Point Index TheoryHammerstein Integral EquationsIndex TheoryMonotone Operator Existence TheoremsMonotone Operator Fixed PointsMonotonicity AssumptionNonlinear Integral Equations
Abstract We present new criteria on the existence of fixed points that combine some monotonicity assumptions with the classical fixed point index theory. As an illustrative application, we use our theoretical results to prove the existence of positive solutions for systems of nonlinear Hammerstein integral equations. An example is also presented to show the applicability of our results. MSC: 47H10, 34B10, 34B18, 45G15, 47H30.
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