Blow-up for nonlinear inequalities with gradient terms and singularities on unbounded sets. (English) Zbl 1357.35157
Summary: 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.
MSC:
| 35J87 | Unilateral problems for nonlinear elliptic equations and variational inequalities with nonlinear elliptic operators |
| 35J62 | Quasilinear elliptic equations |
| 35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
| 35B44 | Blow-up in context of PDEs |
References:
| [1] | C. Azizieh, Existence and apriori estimates for positive solutions of p-Laplace systems,, J. Diff. Eq., 204, 422 (2002) · Zbl 1157.35356 |
| [2] | P. Clement, Positive solutions for a quasilinear system via blow-up,, Comm. PDE, 18, 2071 (1993) · Zbl 0802.35044 |
| [3] | A. Farina, Entire solutions of completely coercive quasilinear elliptic equations,, J. Diff. Eq., 250, 4367 (2011) · Zbl 1225.35097 |
| [4] | A. Farina, Entire solutions of completely coercive quasilinear elliptic equations II,, J. Diff. Eq., 250, 4409 (2011) · Zbl 1225.35098 |
| [5] | E. Galakhov, On blow-up of solutions to differential inequalities with singularities on unbounded sets,, J. Math. Anal. Appl., 408, 102 (2013) · Zbl 1515.35373 |
| [6] | E. Galakhov, Blow-up for nonlinear inequalities with singularities on unbounded sets,, in · Zbl 1326.35138 |
| [7] | E. Mitidieri, A priori estimates and nonexistence of solutions of nonlinear partial differential equations and inequalities,, Proceedings of the Steklov Institute, 234, 1 (2001) · Zbl 1074.35500 |
| [8] | S. Pohozaev, Essentially nonlinear capacities generated by differential operators., Doklady RAN, 357, 592 (1997) · Zbl 0963.35056 |
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