@article{article_549174, title={A CLASS OF THIRD-ORDER BOUNDARY VALUE PROBLEM WITH INTEGRAL CONDITION AT RESONANCE}, journal={Maltepe Journal of Mathematics}, volume={2}, pages={43–54}, year={2020}, DOI={10.47087/mjm.549174}, author={Noureddine, Bouteraa}, keywords={Resonance, Coincidence degree theory, Fredholm operato, One dimensional kernels, Nonlocal boundary value problem}, abstract={<p class="MsoNormal" style="margin-bottom:.0001pt;line-height:normal;"> <span style="font-size:14pt;font-family:CMR8;">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 </span> </p> <p> </p> <p class="MsoNormal" style="margin-bottom:.0001pt;line-height:normal;"> <span style="font-size:14pt;font-family:CMR8;">with integral condition at
resonance case </span> </p> <p> </p> <p class="MsoNormal" style="margin-bottom:.0001pt;line-height:normal;"> <span style="font-size:14pt;font-family:CMR8;">The existence of solution is
etablished via Mawhin’s coincidence degree theory.  </span> <span style="font-size:14pt;line-height:115%;font-family:CMR8;">The results are illustrated with an example </span> <span style="font-size:8pt;line-height:115%;font-family:CMR8;">. </span> </p>}, number={2}, publisher={Hüseyin ÇAKALLI}