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2015, 2015(special): 489-494. doi: 10.3934/proc.2015.0489

Blow-up for nonlinear inequalities with gradient terms and singularities on unbounded sets

Evgeny Galakhov 1, and  Olga Salieva 2,

1. 

Peoples' Friendship University of Russia, Miklukho-Maklaya str. 6, Moscow, 117198, Russian Federation
2. 

Moscow State Technological University , Vadkovsky lane 3a, Moscow, 127055, Russian Federation

Received  September 2014 Revised  September 2015 Published  November 2015

Nonexistence results for nontrivial solutions for some classes of nonlinear partial differential inequalities with gradient terms and coefficients possessing singularities on unbounded sets are obtained.
Keywords: Nonlinear elliptic inequality, unbounded set, singularity, blow-up, gradient terms..
Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C3.
Citation: Evgeny Galakhov, Olga Salieva. Blow-up for nonlinear inequalities with gradient terms and singularities on unbounded sets. Conference Publications, 2015, 2015 (special) : 489-494. doi: 10.3934/proc.2015.0489
References:
[1]

C. Azizieh, P. Clement and E. Mitidieri, Existence and apriori estimates for positive solutions of p-Laplace systems, J. Diff. Eq., 204 (2002), 422-442. Google Scholar

[2]

P. Clement, R. Manasevich and E. Mitidieri, Positive solutions for a quasilinear system via blow-up, Comm. PDE, 18 (1993), 2071-2106. Google Scholar

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A. Farina and J. Serrin, Entire solutions of completely coercive quasilinear elliptic equations, J. Diff. Eq., 250 (2011), 4367-4408. Google Scholar

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A. Farina and J. Serrin, Entire solutions of completely coercive quasilinear elliptic equations II, J. Diff. Eq., 250 (2011), 4409-4436. Google Scholar

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E. Galakhov and O. Salieva, On blow-up of solutions to differential inequalities with singularities on unbounded sets, J. Math. Anal. Appl., 408 (2013), 102-113. Google Scholar

[6]

E. Galakhov and O. Salieva, Blow-up for nonlinear inequalities with singularities on unbounded sets,, in, ().   Google Scholar

[7]

E. Mitidieri and S. 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

[8]

S. Pohozaev, Essentially nonlinear capacities generated by differential operators. Doklady RAN, 357 (1997), 592-594. Google Scholar

show all references

References:
[1]

C. Azizieh, P. Clement and E. Mitidieri, Existence and apriori estimates for positive solutions of p-Laplace systems, J. Diff. Eq., 204 (2002), 422-442. Google Scholar

[2]

P. Clement, R. Manasevich and E. Mitidieri, Positive solutions for a quasilinear system via blow-up, Comm. PDE, 18 (1993), 2071-2106. Google Scholar

[3]

A. Farina and J. Serrin, Entire solutions of completely coercive quasilinear elliptic equations, J. Diff. Eq., 250 (2011), 4367-4408. Google Scholar

[4]

A. Farina and J. Serrin, Entire solutions of completely coercive quasilinear elliptic equations II, J. Diff. Eq., 250 (2011), 4409-4436. Google Scholar

[5]

E. Galakhov and O. Salieva, On blow-up of solutions to differential inequalities with singularities on unbounded sets, J. Math. Anal. Appl., 408 (2013), 102-113. Google Scholar

[6]

E. Galakhov and O. Salieva, Blow-up for nonlinear inequalities with singularities on unbounded sets,, in, ().   Google Scholar

[7]

E. Mitidieri and S. 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

[8]

S. Pohozaev, Essentially nonlinear capacities generated by differential operators. Doklady RAN, 357 (1997), 592-594. Google Scholar

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