ON THE EXISTENCE OF CLASSICAL SOLUTION TO ONE-DIMENSIONAL FOURTH ORDER SEMILINEAR EQUATIONS

Samed J. Aliyev; Maftun N. Heydarova; Arzu G. Aliyeva

Samed J. Aliyev Department of Mathematics and Methods of its Teaching, Faculty of Mechanics and Mathematics , Baku State University, AZ 1148, Z. Khalilov Street, 23, Baku, Azerbaijan
Maftun N. Heydarova Department of Mathematics and Methods of its Teaching, Faculty of Mathematics, Sumgait State University, AZ 5008, District 43, Sumgait, Azerbaijan
Arzu G. Aliyeva Department of Differential Equations Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan, AZ 1141, B. Vagabzade Street,9, Baku, Azerbaijan

Article ID: 2432

Keywords: semilinear equations; mixed problem; classical solution

Abstract

In this paper, we prove the existence in small of classical solution of one-dimensional mixed problem for one class of fourth order semilinear Sobolev type equations by combining the generalized contracted mapping principle with Schauder’s fixed point principle.

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