Multiple Positive Solutions for Singular Semipositone Periodic Boundary Value Problems with Derivative Dependence

By constructing a special cone in C1[0,2π] and the fixed point theorem, this paper investigates second-order singular semipositone periodic boundary value problems with dependence on the first-order derivative and obtains the existence of multiple positive solutions. Further, an example is given to demonstrate the applications of our main results

Applications of Schauder’s Fixed Point Theorem to Semipositone Singular Differential Equations

We study the existence of positive periodic solutions of second-order singular differential equations. The proof relies on Schauder’s fixed point theorem. Our results generalized and extended those results contained in the studies by Chu and Torres (2007) and Torres (2007) . In some suitable weak singularities, the existence of periodic solutions may help

Positive solutions to superlinear semipositone periodic boundary value problems with repulsive weak singular forces

AbstractThis paper is devoted to study the existence of positive solutions to the second-order semipositone periodic boundary value problem x″ + a(t)x = f(t,x), x(0) = x(1), x′(0) = x′(1). Here, f (t, x) may be singular at x = 0 and may be superlinear at x = +∞. Our analysis relies on a fixed-point theorem in cones