SOLVABILITY OF THE BOUNDARY PROBLEMS FOR THE QUASILINEAR SECOND ORDER EQUATIONS WITH PARAMETER IN THE RIGHT-HAND SIDE

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Published: Dec 25, 2018
Keywords:
boundary value problems, quasilinear second-order equation, Green's function, fixed point, Schauder theorem

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А. Vorontsova
Vasyl` Stus Donetsk National University, Vinnytsia
К. Buryachenko
Vasyl` Stus Donetsk National University, Vinnytsia

Abstract

The paper is devoted to the problem of solvability of the first boundary value problem for a quasilinear second-order equation with a parameter in the right-hand side and a power nonlinearity of arbitrary order. Using the operator methods (inverse operator method, fixed point method), the theorem for the existence of a classical solution of a problem is proved. The methodological and theoretical aspects of the application of the obtained result for the solving of the corresponding problems are given.

Article Details

Issue
Vol. 1 No. 1 (2018)
Section
Mathematical and Calculation Physics
Author Biographies

А. Vorontsova, Vasyl` Stus Donetsk National University, Vinnytsia

Master's Degree

К. Buryachenko, Vasyl` Stus Donetsk National University, Vinnytsia

Department of Mathematical Analysis and Differential Equations

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