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

Main Article Content

А. Vorontsova
К. Buryachenko

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

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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