«FarDU ilmiy xabarlari» Volume 31 Issue 6 (2025)
A UNIQUE SOLUTION OF A BOUNDARY VALUE PROBLEM FOR AN ELLIPTIC-HYPERBOLIC TYPE EQUATION
Nishonova, Shaxnozaxon
Abstract
<p>In this paper, the unique solution of a boundary value problem for a differential equation of elliptic-hyperbolic type is studied. The purpose of the research is to demonstrate the existence and uniqueness of the solution for the given mixed-type equation. By applying the Gauss-Ostrogradsky formula, as well as the properties of the Fredholm integral equation and the energy integral method, the existence and uniquenessof the solution are proved. The results show that the kernel function is continuos and bounded throughout the entire interval, which guarantees the existence of a unique solution to the corresponding integral equation. In conclusion, it can be stated that the proposed analytical approach for elliptic-hyperbolic type differential equations provides a theoretically consistent and paractically effective method for solving boundary value problems of mixed type. The obtained results can be applied to the study and solution of boundary value problems for mixed elliptic and hyperbolic equations.</p>
Fredgolm integral tenglamasiGrin funksiyasiBessel funksiyasiGauss-Ostragradskiy formulasiFredgolm integral tenglamasiGrin funksiyasiBessel funksiyasiGauss-Ostragradskiy formulasi
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