George Smyrlis

Solvability for a third-order three-point BVP on time scales

We are concerned with the existence of a nontrivial solution to a nonlinear third-order three-point boundary-value problem on general time scales. Using the corresponding Green function, without a non-negative or monotone-type assumption on the nonlinearity, we obtain sufficient conditions for the existence of at least one nontrivial solution, using the Leray-Schauder nonlinear alternative theorem. This paper extends recent results in differential equations to difference equations, quantum equations, and general dynamic equations on time scales.

On a singular semilinear elliptic problem: multiple solutions via critical point theory

We study existence and multiplicity of solutions of a semilinear elliptic problem involving a singular term. Combining various techniques from critical point theory, under different sets of assumptions, we prove the existence of

An Overview on Singular Nonlinear Elliptic Boundary Value Problems

k

Resonant Robin problems with indefinite and unbounded potential

solutions (

Strongly resonant Robin problems with idefinite and unbounded potential

k\in\mathbb N

Positive solutions for nonlinear nonhomogeneous parametric equations

) or infinitely many weak solutions.

Positive solutions to a singular third-order three-point boundary value problem with an indefinitely signed Green’s function

We give a survey of old and recent results concerning existence and multiplicity of positive solutions (classical or weak) to nonlinear elliptic equations with singular nonlinear terms of the form

On nonlinear nonhomogeneous resonant Dirichlet equations

\displaystyle \left \{ \begin {array}{ll} -\varDelta _p u= f(x,u)+ u^{-\gamma }, & \mbox{ in }\ \varOmega \\ u>0, & \mbox{ in }\ \varOmega \\ u=0, & \mbox{ on }\ \partial \ \varOmega , \end {array} \right .