Positive solutions for second-order differential equations with singularities and separated integral boundary conditions

Abstract

We study the existence of positive solutions for second-order differential equations with separated integral boundary conditions. The nonlinear part of the equation involves the derivative and may be singular for the second and third space variables. The result ensures existence of a positive solution when the parameters are in certain ranges. The proof depends on general properties of the associated Green's function and the Krasnosel'skii–Guo fixed point theorem applied to a perturbed Hammerstein integral operator. Both numerical and analytical examples are constructed to illustrate applications of the theorem to a group of equations. The result generalizes previous work.

Keywords

• fixed point
• green's function
• hammerstein integral operator
• positive solution
• singular boundary value problem