References

  1. Adams R.A. Sobolev Spaces. Academic Press, New York, 1975.
  2. Antontsev S.N., Rodrigues J.F. On stationary thermo-rheological viscous flows. Ann. Univ. Ferrara Sez. VII Sci. Mat. 2006, 52 (1), 19-36. doi: 10.1007/s11565-006-0002-9
  3. Berestycki H., Nirenberg L. Some qualitive properties of solutions of semilinear elliptic equations in cylindrical domains. Analysis, Academic Press Boston, 1990.
  4. Brezis H. Points critiques dans les problémes variationnels sans compacité. Séminaire Bourbaki 1989, 698 (5), 239-256.
  5. Chen Y., Levine S., Rao M. Variable exponent, linear growth functionals in image restoration. SIAM J. Appl. Math. 2006, 66 (4), 1383-1406. doi: 10.1137/050624522
  6. Diening L., Harjulehto P., Hastö P., Ružička M. Lebesgue and Sobolev Spaces with Variable Exponents. Lecture Notes in Mathematics, Springer, Heidelberg 2011. doi: 10.1007/978-3-642-18363-8
  7. Dubinskiĩ Yu.A. Weak convergence in nonlinear elliptic and parabolic equations. Mat. Sb., 1965, 67 (109), 609-642.
  8. Dubinskiĩ Yu.A. Nonlinear elliptic and parabolic equations. J. Math. Sci. 1979, 12, 475-554. doi: 10.1007/BF01089137 (translation of Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. 1976, 9, 5-130. (in Russian))
  9. Fan X., Zhao D. On the spaces $L^{p\left( x\right) }(\Omega)$ and $W^{k,p\left( x\right)}(\Omega)$. J. Math. Anal. Appl. 2001, 263 (2), 424-446. doi: 10.1006/jmaa.2000.7617
  10. Kováčik O., Rákosnĩk J. On spaces $L^{p\left( x\right)}$ and $W^{k,p\left( x\right) }$. Czechoslovak Math. J. 1991, 41 (4), 592-618.
  11. Lions J.L. Quelques méthodes de résolution des probl\`emes aux limites non linéaires. Dunod and Gauthier-Villars, Paris, 1969.
  12. Luckhaus S., Passo R. Dal. A degenerate diffusion problem not in divergence form. J. Differential Equations 1987, 69 (1), 1-14.
  13. Musielak J. Orlicz Spaces and Modular Spaces. Lecture Notes in Mathematics, Springer-Verlag, Berlin, 1983. doi: 10.1007/BFb0072210
  14. Oleĩnik O.A. The mathematical problems of the theory of the boundary layer. Russ. Math. Surv. 1968, 23 (3), 3-65. (in Russian)
  15. Pohozaev S.I. Nonlinear operators which have a weakly closed range of values and quasilinear elliptic equations. Mat. Sb. 1969, 78, 237-259.
  16. Rao M.M. Measure Theory And Integration. John Wiley & Sons, New York, 1984.
  17. Ruzicka M. Electrorheological Fluids: Modeling and Mathematical Theory. In Lecture Notes in Mathematics, Springer-Verlag, Berlin, 2000. doi: 10.1007/BFb0104029
  18. Samokhin B.N. The system of equations of a boundary layer of a pseudoplastic fluid. Dokl. Akad. Nauk SSSR 1973, 210 (5), 1043-1046. (in Russian)
  19. Sert U., Soltanov K.N. On Solvability of a Class of Nonlinear Elliptic type Equation with Variable Exponent. J. Appl. Anal. Comput. 2017, 7 (3), 1139-1160. doi: 10.11948/2017071
  20. Sert U., Soltanov K.N. Solvability of nonlinear elliptic type equation with two unrelated non standard growths. J. Korean Math. Soc. 2018, 55 (6), 1337-1358. doi: 10.4134/JKMS.j170691
  21. Soltanov K.N. Imbedding theorems of the nonlinear spaces and solvability some nonlinear noncoercive equations. Preprint, VINITI, N3696-B 91, Moscow, 1991, 71 pp. (in Russian)
  22. Soltanov K.N. Some embedding theorems and its applications to nonlinear equations. Differ. Uravn. 1984, 20 (12), 2181-2184. (in Russian)
  23. Soltanov K.N. Some applications of the nonlinear analysis to the differential equations. ELM, Baku, 2002. (in Russian)
  24. Soltanov K.N. Periodic solutions some nonlinear parabolic equations with implicit degenerate. Dokl. Akad. Nauk SSSR 1975, 222 (2), 291-294. (in Russian)
  25. Soltanov K.N. Embedding theorems for nonlinear spaces and solvability of some nonlinear noncoercive equations. Proc. Inst. Math. Mech. Natl. Acad. Sci. Azerb. 1996, 5, 72-103. (in Russian)
  26. Soltanov K.N. Some nonlinear equations of the nonstable filtration type and embedding theorems. Nonlinear Anal. 2006, 65 (11), 2103-2134. doi: 10.1016/j.na.2005.11.053
  27. Soltanov K.N. Existence and nonexistence of the global solutions some nonlinear elliptic-parabolic equations. Differ. Uravn. 1993, 29 (4), 646-661. (in Russian)
  28. Soltanov K.N. On nonlinear equations of the form $ F\left( x,u,Du,\Delta u\right) =0$. Sb. Math. 1995, 80 (2), 367-392.
  29. Soltanov K.N. Solvability nonlinear equations with operators the form of sum the pseudomonotone and weakly compact. Dokl. Akad. Nauk 1992, 324 (5), 944-948.
  30. Soltanov K.N. Solvability of certain parabolic problems with faster-growing-than-power nonlinearities. Mat. Zametki 1982, 32 (6), 909-923.
  31. Soltanov K.N. Smooth solvability some quasielliptic problems. Izv. Akad. Nauk Azerbaĩdzhan. 1979, 2, 61-67. (in Russian)
  32. Soltanov K.N. Some Boundary Problem for Emden-Fowler Type Equations, Function Spaces. Differential Operators and Nonlinear Analysis, ``FSDONA'', Praha, Czech Republic, May, 2005, Math. Inst. Acad. Sci., Praha, Czech Republic, 2005, 311-318.
  33. Soltanov K.N., Akmedov M. Solvability of Equation of Prandtl-von Mises type, Theorems of Embedding. Trans. Natl. Acad. Sci. Azerb. Ser. Phys.-Tech. Math. Sci. 2017, 37 (1), 143-168.
  34. Soltanov K.N., Sprekels J. Nonlinear equations in nonreflexive Banach spaces and fully nonlinear equations. Adv. Math. Sci. Appl. 1999, 9 (2), 939-972.
  35. Tsutsumi T., Ishiwata M. Regional blow-up of solutions to initial boundary value problem for $u_{t}=u^{\delta }\left( \Delta u+u\right) $. Proc. Roy. Soc. Edinburgh Sect. A 1997, 127 (4), 871-887.
  36. Walter W. Existence and convergence theorems for the boundary layer equations based on the line method. Arch. Ration. Mech. Anal. 1970, 39 (3), 169-188.
  37. Wiegner M. A degenerate diffusion equation with a nonlinear source term. Nonlinear Anal. 1997, 28 (12), 1977-1995. doi: 10.1016/S0362-546X(96)00027-2
  38. Zhikov V.V. On some variational problems. Russ. J. Math. Phys. 1997, 5 (1), 105-116.