A CLASS OF THIRD-ORDER BOUNDARY VALUE PROBLEM WITH INTEGRAL CONDITION AT RESONANCE

Year 2020, , 43 - 54, 12.11.2020

Bouteraa Noureddine

https://doi.org/10.47087/mjm.549174

Cited By: 2

Abstract

In this paper, we consider third-order boundary value problem
with, Dirichlet, Neumann and integral conditions at resonance case, where the
kernel’s dimension of the ordinary differential operator is equal to one and the
ordinary differential equation which can be written as the abstract equation
Lu = Nu, called semilinear form, where L is a linear Fredholm operator of
index zero, and N is a nonlinear operator. First, we prove a priori estimates,
and then we use Mawhin’s coincidence degree theory to deduce the existence
of solutions. One important ingredient to be able to apply this abstract results
(Mawhin’s coincidence degree theory) is proving the Fredholm property of the
operator L. An example is also presented to illustrate the effectiveness of the
main results

with integral condition at
resonance case

The existence of solution is
etablished via Mawhin's coincidence degree theory. The results are illustrated with an example.

Keywords

Resonance, Coincidence degree theory, Fredholm operato, One dimensional kernels, Nonlocal boundary value problem

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