Absence of solutions for some nonhomogeneous elliptic inequalities
Contemporary Mathematics. Fundamental Directions, Proceedings of the S.M. Nikolskii Mathematical Institute of RUDN University, Tome 65 (2019) no. 4, pp. 605-612
E. I. Galakhov; O. A. Salieva. Absence of solutions for some nonhomogeneous elliptic inequalities. Contemporary Mathematics. Fundamental Directions, Proceedings of the S.M. Nikolskii Mathematical Institute of RUDN University, Tome 65 (2019) no. 4, pp. 605-612. http://geodesic.mathdoc.fr/item/CMFD_2019_65_4_a3/
@article{CMFD_2019_65_4_a3,
     author = {E. I. Galakhov and O. A. Salieva},
     title = {Absence of solutions for some nonhomogeneous elliptic inequalities},
     journal = {Contemporary Mathematics. Fundamental Directions},
     pages = {605--612},
     year = {2019},
     volume = {65},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2019_65_4_a3/}
}
TY  - JOUR
AU  - E. I. Galakhov
AU  - O. A. Salieva
TI  - Absence of solutions for some nonhomogeneous elliptic inequalities
JO  - Contemporary Mathematics. Fundamental Directions
PY  - 2019
SP  - 605
EP  - 612
VL  - 65
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/CMFD_2019_65_4_a3/
LA  - ru
ID  - CMFD_2019_65_4_a3
ER  - 
%0 Journal Article
%A E. I. Galakhov
%A O. A. Salieva
%T Absence of solutions for some nonhomogeneous elliptic inequalities
%J Contemporary Mathematics. Fundamental Directions
%D 2019
%P 605-612
%V 65
%N 4
%U http://geodesic.mathdoc.fr/item/CMFD_2019_65_4_a3/
%G ru
%F CMFD_2019_65_4_a3

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

By means of the modified method of test functions, we obtain sufficient conditions of absence of nontrivial solutions for some classes of semilinear elliptic inequalities of higher order and quasilinear elliptic inequalities containing nonhomogeneous terms (independent of the unknown function).

[1] E. Mitidieri, S. I. Pohozaev, “Liouville theorems for some classes of nonlinear nonlocal problems”, Proc. Math. Inst. Russ. Acad. Sci., 248, 2005, 158–178 (in Russian) | Zbl

[2] S. I. Pohozaev, “Essentially nonlinear capacities generated by differential operators”, Rep. Russ. Acad. Sci., 357 (1997), 592–594 (in Russian) | Zbl

[3] V. Galaktionov, E. Mitidieri, S. Pohozaev, Blow-up for higher-order parabolic, hyperbolic, dispersion and Schrödinger equations, Chapman and Hall/CRC, Boca Raton, 2014 | MR

[4] E. Galakhov, O. Salieva, “On blow-up of solutions to differential inequalities with singularities on unbounded sets”, J. Math. Anal. Appl., 408 (2013), 102–113 | DOI | MR | Zbl

[5] O. Salieva, “On nonexistence of solutions to some nonlinear parabolic inequalities”, Commun. Pure Appl. Anal., 16:3 (2017), 843–853 | DOI | MR | Zbl