TY  - JOUR
T1  - A CLASS OF THIRD-ORDER BOUNDARY VALUE PROBLEM WITH INTEGRAL CONDITION AT RESONANCE
AU  - Noureddine, Bouteraa
PY  - 2020
DA  - November
Y2  - 2020
DO  - 10.47087/mjm.549174
JF  - Maltepe Journal of Mathematics
PB  - Hüseyin ÇAKALLI
WT  - DergiPark
SN  - 2667-7660
SP  - 43
EP  - 54
VL  - 2
IS  - 2
LA  - en
AB  - In this paper, we consider third-order boundary value problemwith, Dirichlet, Neumann and integral conditions at resonance case, where thekernel’s dimension of the ordinary differential operator is equal to one and theordinary differential equation which can be written as the abstract equationLu = Nu, called semilinear form, where L is a linear Fredholm operator ofindex 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 existenceof solutions. One important ingredient to be able to apply this abstract results(Mawhin’s coincidence degree theory) is proving the Fredholm property of theoperator L. An example is also presented to illustrate the effectiveness of themain resultswith integral condition atresonance caseThe existence of solution isetablished via Mawhin's coincidence degree theory.The results are illustrated with an example.
KW  - Resonance
KW  - Coincidence degree theory
KW  - Fredholm operato
KW  - One dimensional kernels
KW  - Nonlocal boundary value problem
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UR  - https://doi.org/10.47087/mjm.549174
L1  - https://dergipark.org.tr/en/download/article-file/687936
ER  -