Initial-boundary value problem for doubly nonlinear integro-differential equations with variable exponents of nonlinearity

1Buhrii, OM
1Ivan Franko National University of Lviv
Dopov. Nac. akad. nauk Ukr. 2017, 2:3-9
Section: Mathematics
Language: Ukrainian

We consider the initial-boundary value problem for doubly nonlinear parabolic equations with variable exponents of nonlinearity perturbed by a generator of the jump process arising from the theory of European options. The existence theorem for the problem is proved.

Keywords: doubly nonlinear parabolic equation, European option, integro-differential equation, jump-diffusion process, variable exponent of nonlinearity
  1. Gajewski, H., Groger, K., Zacharias, K. (1978). Nonlinear operator equations and operator differential equations. Mos cow: Mir (in Russian).
  2. Merton, R. C. (1976). J. Finan. Econ., 3, pp.125-144.
  3. Bokalo, T. M., Buhrii, O. M. (2011). Ukr. Math. J., 63, Iss. 5, pp. 612-628 (in Ukrainian).
  4. Antontsev, S., Shmarev, S. (2015). Evolution PDEs with nonstandard growth conditions, Existence, uniqueness, localization, blow-up, Atlantis Studies in Differential Equations, Vol. 4. Paris: Atlantis Press.
  5. Souplet, Ph. (1999). J. Differ. Equat., 153, pp. 374-406.
  6. Bokalo, M., Dmytriv, V. (2001). Visnyk Lviv Univ. Ser. Mech.-Math., Iss. 59, pp. 84-101 (in Ukrainian).
  7. Pinasco, J. P. (2009). Nonlinear Analysis, 71, pp. 1094-1099.
  8. Buhrii, O., Buhrii, M. (2016). Visnyk Lviv Univ. Ser. Mech.-Math., Iss. 81, pp. 61-84.
  9. Briani, M., Natalini, R., Russo, G. (2007). Calcolo, 44, Iss. 1, pp. 33-57.
  10. Cifani, S., Jakobsen, E. R., Karlsen, K. H. (2011). BIT, 51, Iss. 4, pp. 809-844.
  11. Ladyzhenskaya, O. A., Uraltseva, N. N. (1973). Linear and quasilinear elliptic equations. Moscow: Nauka (in Russian).
  12. Dunford, N., Schwartz, J. T. (1962). Linear Operators, Pt. I: General Theory. Moscow: Izd-vo Inostr. lit. (in Russian).
  13. Kovacik, O., Rakosnik, J. (1991). Czech. Math. J., 41 Iss.116, pp. 592-618.
  14. Evans, L. C. (1998). Partial differential equations, Graduate Studies in Mathematics, Vol. 19. Providence, RI: Amer. Math. Soc.,
  15. Galewski, M. (2006). Georgian Math. J., 13, Iss. 2, pp. 261-265.