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Existence of solutions for a three-point Hadamard fractional resonant boundary value problem

Gholami Yousef

Journal of Applied Analysis

2023

Vol. 29, nr 1

31--47

This article focuses on the creation of an existence theorem for a fully nonlinear Hadamard fractional boundary value problem subject to special three-point boundary conditions. By making use of the coincidence degree theory, it is proved that our governing problem makes resonance, that is, the linear part of the differential operator is non-invertible (equally, the corresponding linear problem has at least one nontrivial solution). Constructing some hypotheses on the linear part of the differential operator, nonlinearities and boundary conditions, we give an existence criterion for at least one solution of the fractional-order resonant boundary value problem under study. At the end, a numerical example is presented to illustrate the obtained theoretical results.

Multiple solutions of boundary value problems on time scales for φ-laplacian operator

Amster Pablo, Kuna Mariel Paula, Santos Dionicio Pastor

Opuscula Mathematica

2020

Vol. 40, no. 4

405--425

We establish the existence and multiplicity of solutions for some boundary value problems on time scales with a y-Laplacian operator. For this purpose, we employ the concept of lower and upper solutions and the Leray-Schauder degree. The results extend and improve known results for analogous problems with discrete p-Laplacian as well as those for boundary value problems on time scales.

On one method for constructing a dynamical mesh of nonlinear quasiperfect processes in deformable anisotropic media

Bomba A., Kashtan S.

Journal of Applied Computer Science

2004

Vol. 12, nr 2

7-21

A new algorithm has been developed for numerical solving inverse nonlinear boundary value problems on quasiconformal mapping in anisotropic media, which are curvilinear tetragons limited by lines of a flow and equipotential lines under action of a potential gradient tensor. The dynamical mesh has been constructed and the velocity field of the domain has been calculated.