Positive solutions for second-order differentialequations with singularities and separated integralboundary conditions

摘要

We study the existence of positive solutions for second-order differentialequations with separated integral boundary conditions. The nonlinear part of theequation involves the derivative and may be singular for the second and third spacevariables. The result ensures existence of a positive solution when the parameters arein certain ranges. The proof depends on general properties of the associated Green’sfunction and the Krasnosel’skii–Guo fixed point theorem applied to a perturbed Hammerstein integral operator. Both numerical and analytical examples are constructed toillustrate applications of the theorem to a group of equations. The result generalizesprevious work.