First-order partial differential equations with variable coefficients in the class of separately differentiable functions(in Ukrainian)

V. I. Myronyk, V. V. Mykhaylyuk
Yuriy Fedkovych Chernivtsi National University
Let $\alpha$ be a function, which have a primitive on $\mathbb{R}$. It is obtained a general solutions of differential equation $\frac{\partial f}{\partial x}(x,y)+\alpha (x)\frac{\partial f}{\partial y}(x,y)=0$ in the class of separately differentiable functions.
separately differentiable functions; partial differential equations
1. Baire R. Sur les fonctions de variables relles// Annali di mat. pura ed appl. 1899. V.3, P. 1123.

2. Banakh T., Mykhaylyuk V. Separately twice differentiable functions and the equation of string oscillation// Real Anal. Exch. 2012/2013. V.38, 1. P. 133156.

3. Breckenridge J.C., Nishiura T. Partial continuity, quasicontinuiuty and Baire spaces// Bull. Inst. Acad. Sinica. 1976. V.4, 2. P. 191203.

4. Bruckner A.M., Petruska G., Preiss O., Thomson B.S. The equation $u_xu_y=0$ factors// Acta. Math. Hung. 1991. V.57 34. P. 275278.

5. Chernoff P.R., Royden H.F. The equation $\frac{\partial f}{\partial x}=\frac{\partial f}{\partial y}$ // Am. Math. Mon. 1975. V.82, 5. P. 530531.

6. Kalancha A.K., Maslyuchenko V.K. Generalization of Bruckner-Petruska-Preiss-Thomson theorem// Mat. Stud. 1999. V.11, 1. P. 4852. (in Ukrainian)

7. Maslyuchenko V.K., Mykhaylyuk V.V. Solving of partial differential equations under minimal conditions// J. Math. Phys., Anal., Geom. 2008. V.4, 2. P. 252266.

8. Maslyuchenko V.K. A property of partial derivatives// Ukr. Math. J. 1987. V.39, 4. P. 529531. (in Russian)

9. Myronyk V.I., Mykhaylyuk V.V. First-order linear partial differential equations in the class of separately differentiable functions// Carpathian Mathematical Publications. 2013. V.5, 1. P. 8993.

10. Tolstov H.P. On pathional derivatives// Izvestia AN SSSR, Ser. Matem. 1949. V.13, 5. P. 425446. (in Russian)

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