# American Institute of Mathematical Sciences

May  2017, 16(3): 843-853. doi: 10.3934/cpaa.2017040

## On nonexistence of solutions to some nonlinear parabolic inequalities

 Moscow State Technological Institute "Stankin", Vadkovsky lane 3a, Moscow, 127055, Russia

Received  May 2016 Revised  December 2016 Published  February 2016

Fund Project: The author is supported by RFBR grant 14-01-00736. She also thanks the anonymous referee for her/his helpful comments.

We obtain sufficient conditions for nonexistence of positive solutions to some nonlinear parabolic inequalities with coefficients possessing singularities on unbounded sets.

Citation: Olga Salieva. On nonexistence of solutions to some nonlinear parabolic inequalities. Communications on Pure & Applied Analysis, 2017, 16 (3) : 843-853. doi: 10.3934/cpaa.2017040
##### References:
 [1] H. Brezis and X. Cabré, Some simple nonlinear PDE's without solutions, Boll. Un. Mat. Ital. B: Artic. Ric. Mat., 8 (1998), 223-262.   Google Scholar [2] E. Galakhov, Some nonexistence results for quasi-linear PDE's, Commun. Pure Appl. Anal., 6 (2007), 141-161.  doi: 10.3934/cpaa.2007.6.141.  Google Scholar [3] E. Galakhov and O. Salieva, On blow-up of solutions to differential inequalities with singularities on unbounded sets, JMAA, 408 (2013), 102-113.  doi: 10.1016/j.jmaa.2013.05.069.  Google Scholar [4] E. Galakhov and O. Salieva, Blow-up of solutions of some nonlinear inequalities with singularities on unbounded sets, Math. Notes, 98 (2015), 222-229.  doi: 10.4213/mzm10622.  Google Scholar [5] E. Mitidieri and S. I. Pohozaev, A priori estimates and nonexistence of solutions of nonlinear partial differential equations and inequalities, Proceedings of the Steklov Institute, 234 (2001), 1-383.   Google Scholar [6] S. I. Pohozaev, Essentially nonlinear capacities induced by differential operators, Dokl. RAN, 357 (1997), 592-594.   Google Scholar [7] G. M. Wei, Nonexistence of global solutions for evolutional p-Laplace inequalities with singular coefficients, J. Math. Anal. Appl., 28A (2007), 387-394.   Google Scholar [8] B. F. Zhong and X. Lijun, Nonexistence of global solutions for evolutional p-Laplace inequalities with singular coefficients, Journal of Inequalities and Applications, 62 (2014).   Google Scholar

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##### References:
 [1] H. Brezis and X. Cabré, Some simple nonlinear PDE's without solutions, Boll. Un. Mat. Ital. B: Artic. Ric. Mat., 8 (1998), 223-262.   Google Scholar [2] E. Galakhov, Some nonexistence results for quasi-linear PDE's, Commun. Pure Appl. Anal., 6 (2007), 141-161.  doi: 10.3934/cpaa.2007.6.141.  Google Scholar [3] E. Galakhov and O. Salieva, On blow-up of solutions to differential inequalities with singularities on unbounded sets, JMAA, 408 (2013), 102-113.  doi: 10.1016/j.jmaa.2013.05.069.  Google Scholar [4] E. Galakhov and O. Salieva, Blow-up of solutions of some nonlinear inequalities with singularities on unbounded sets, Math. Notes, 98 (2015), 222-229.  doi: 10.4213/mzm10622.  Google Scholar [5] E. Mitidieri and S. I. Pohozaev, A priori estimates and nonexistence of solutions of nonlinear partial differential equations and inequalities, Proceedings of the Steklov Institute, 234 (2001), 1-383.   Google Scholar [6] S. I. Pohozaev, Essentially nonlinear capacities induced by differential operators, Dokl. RAN, 357 (1997), 592-594.   Google Scholar [7] G. M. Wei, Nonexistence of global solutions for evolutional p-Laplace inequalities with singular coefficients, J. Math. Anal. Appl., 28A (2007), 387-394.   Google Scholar [8] B. F. Zhong and X. Lijun, Nonexistence of global solutions for evolutional p-Laplace inequalities with singular coefficients, Journal of Inequalities and Applications, 62 (2014).   Google Scholar
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