John R. Graef

Positive solutions for a fractional boundary value problem

We obtain a new upper estimate for the Green’s function associated with a higher order fractional boundary value problem. As an application of this result, criteria for the existence of positive solutions of the problem are then established.

Local attractivity and stability analysis of a nonlinear quadratic fractional integral equation

The authors prove two local attractivity and asymptotic stability results for a hybrid functional nonlinear fractional integral equation under weak Lipschitz and compactness type conditions. It is shown that comparable solutions of the equation are uniformly locally ultimately attractive and asymptotically stable on unbounded intervals of the real line. Their proofs rely on a recent measure theoretic fixed point theorem of Dhage.

Three solutions for second-order impulsive differential inclusions with Sturm-Liouville boundary conditions via nonsmooth critical point theory

A second-order impulsive differential inclusion with Sturm-Liouville boundary conditions is studied. By using a nonsmooth version of a three critical point theorem of Ricceri, the existence of three solutions is obtained.

Multiple solutions of boundary value problems : a variational approach

Mathematical Preliminaries Sturm-Liouville Problems, Multiple Solutions, Infinitely Many Solutions Multi-Point Problems, Multiple Solutions, Two Parameter Systems, Existence by the Dual Action Principle Impulsive Problems, Existence of Infinitely Many Solutions, Anti-Periodic Solutions Partial Differential Equations, Kirchhoff-type Problems with Two Parameters, Biharmonic Systems, Elliptic Problems with a p(x)-biharmonic Operator Difference Equations, Periodic Problems with One and Two Parameters, Periodic Problems, Multi-point Problems with Several Parameters, Homoclinic Solutions, Anti-periodic Solutions