Nickolai Kosmatov

A multiplicity result for a boundary value problem with infinitely many singularities

Abstract We consider the second order boundary value problem −u″(t)=a(t)f(u(t)), 0 where a(t)∈Lp[0,1] for some p⩾1 and has countably many singularities in [0,1/2). We show that there exist countably many positive solutions using Holders inequality and Krasnoselskiis fixed point theorem for operators on a cone.

Eigenvalue comparison for fractional boundary value problems with the Caputo derivative

We apply the theory for u0-positive operators to obtain eigenvalue comparison results for a fractional boundary value problem with the Caputo derivative.

Singular Conjugate Boundary Value Problems on a Time Scale

Let 𝕊 be a time scale symmetric about 1/2. Let be right dense and define The conjugate nonlinear boundary value problem where a(t) is singular at and f satisfies certain growth conditions, is shown to have infinitely many solutions using Krasnoselskis fixed point theorem.

Integral equations of fractional order in Lebesgue spaces

Abstract We discuss solvability of a nonlinear Riemann-Liouville integral equation in Lebesgue spaces. We treat the Volterra equations of the first and the second types by applying boundedness criteria for the Riemann-Liouville integral operator. The existence of a solution to integral equations will follow from the Leray-Schauder Nonlinear Alternative.