Existence of positive solutions for non local p-Laplacian thermistor problems on time scales

We make use of the Guo-Krasnoselskii fixed point theorem on cones to prove existence of positive solutions to a non local p-Laplacian boundary value problem on time scales arising in many applications. © 2007 Victoria University. All rights reserved.CEOCFCTFEDER/POCTISFRH/BPD/20934/200

Existence and regularity of optimal solution for a dead oil isotherm problem

We study a system of nonlinear partial differential equations resulting from the traditional modelling of oil engineering within the framework of the mechanics of a continuous medium. Existence and regularity of the optimal solutions for this system is established. © Balkan Society of Geometers, Geometry Balkan Press 2007.CEOCFCTp SFRH/BPD/20934/200

Existence and uniqueness of solutions to functional integro-differential fractional equations

Using a fixed point theorem in a Banach algebra, we prove an existence result for a fractional functional differential equation in the Riemann- Liouville sense. Dependence of solutions with respect to initial data and an uniqueness result are also obtained

Regularity of solutions to higher-order integrals of the calculus of variations

We obtain new regularity conditions for problems of calculus of variations with higher-order derivatives. As a corollary, we get non-occurrence of the Lavrentiev phenomenon. Our main regularity result asserts that autonomous integral functionals with a Lagrangian having coercive partial derivatives with respect to the higher-order derivatives admit only minimisers with essentially bounded derivatives