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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.

Periodic solutions of first-order functional differential equations with supper-linear nonliearities

Liu Y.

Fasciculi Mathematici

2007

Nr 38

57-74

The existence results for periodic solutions concerning first-order functional differential equation are proved. The methods are based upon the coincidence degree theory by Mawhin. The results obtained are new. Examples, that can not be solved by known theorems, are given to illustrate the main results.