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Nonexistence of solutions for nonlinear differential inequalities with gradient nonlinearities
1. | School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024, China, China |
References:
[1] |
E. Galakhov, Some nonexistence results for quasilinear PDE's, Commun. Pure Appl. Anal., 6 (2007), 141-161.
doi: 10.1002/cpa.3160390306. |
[2] |
E. Mitidieri and S. I. Pohozaev, Absence of positive solutions for quasilinear elliptic problems in $\mathbb{R}^N2$, Proc. Steklov Inst. Math., 227 (1999), 186-216. |
[3] |
E. Mitidieri and S. I. Pohozaev, Nonexistence of weak solutions for some degenerate elliptic and parabolic problems on $R^n$, J. Evol. Equ., 1 (2001), 189-220.
doi: 10.1007/PL00001368. |
[4] |
E. Mitidieri and S. I. Pohozaev, A priori estimates and the absence of solutions of nonlinear partial differential equations and inequalities, Proc. Steklov Inst. Math., 234 (2001), 1-362. |
[5] |
E. Mitidieri and S. I. Pohozaev, Towards a unified approach to nonexistence of solutions for a class of differential inequalities, Milan J. Math., 72 (2004), 129-162.
doi: 10.1007/s00032-004-0032-7. |
[6] |
G. Karisti, On the absence of solutions of systems of quasilinear elliptic inequalities, Differ. Equs., 38 (2002), 375-383.
doi: 10.1023/A:1016061909813. |
[7] |
G. G. Laptev, On the absence of solutions to a class of singular semilinear differential inequalities, Proc. Steklov Inst. Math., 232 (2001), 216-228. |
[8] |
H. Brezis and X. Cabré, Some simple nonlinear PDE's without solutions, Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat., 1 (1998), 223-262. |
[9] |
J. Serrin and H. Zou, Cauchy-Liouville and universal boundedness theorems for quasilinear elliptic equations and inequalities, Acta Math., 189 (2002), 79-142.
doi: 10.1007/BF02392645. |
[10] |
J. Serrin, Entire solutions of quasilinear elliptic equations, J. Math. Anal. Appl., 352 (2009), 3-14.
doi: 10.1016/j.jmaa.2008.10.036. |
[11] |
L. D'Ambrosio, Liouville theorems for anisotropic quasilinear inequalities, Nonlinear Anal., 70 (2009), 2855-2869.
doi: 10.1016/j.na.2008.12.028. |
[12] |
L. D'Ambrosio and E. Mitidieri, Nonnegative solutions of some quasilinear elliptic inequalities and applications, Mat. Sb., 201 (2010), 1-20.
doi: 10.1070/SM2010v201n06ABEH004094. |
[13] |
L. D'Ambrosio and E. Mitidieri, A priori estimates, positivity results, and nonexistence theorems for quasilinear degenerate elliptic inequalities, Adv. Math., 224 (2010), 967-1020.
doi: 10.1016/j.aim.2009.12.017. |
[14] |
M. F. Bidaut-Véron and S. Pohozaev, Nonexistence results and estimates for some nonlinear elliptic problems, J. Anal. Math., 84 (2001), 1-49.
doi: 10.1007/BF02788105. |
[15] |
R. Filippucci, Nonexistence of positive weak solutions of elliptic inequalities, Nonlinear Anal., 70 (2009), 2903-2916.
doi: 10.1016/j.na.2008.12.018. |
[16] |
R. Filippucci, P. Pucci and M. Rigoli, Non-existence of entire solutions of degenerate elliptic inequalities with weights, Arch. Ration. Mech. Anal., 188 (2008), 155-179.
doi: 10.1017/s00205-007-0081-5. |
[17] |
R. Filippucci, P. Pucci and M. Rigoli, On weak solutions of nonlinear weighted $p$-Laplacian elliptic inequalities, Nonlinear Anal., 70 (2009), 3008-3019.
doi: 10.1016/j.na.2008.12.031. |
[18] |
R. Filippucci, P. Pucci and M. Rigoli, On entire solutions of degenerate elliptic differential inequalities with nonlinear gradient terms, J. Math. Anal. Appl., 356 (2009), 689-697.
doi: 10.1016/j.jmaa.2009.03.050. |
[19] |
R. Filippucci, P. Pucci and M. Rigoli, Nonlinear weighted $p$-Laplacian elliptic inequalities with gradient terms, Commun. Contemp. Math., 12 (2010), 501-535.
doi: 10.1142/S0219199710003841. |
[20] |
S. I. Pohozaev, A general approach to the theory of the nonexistence of global solutions of nonlinear partial differential equations and inequalities, Proc. Steklov Inst. Math., 236 (2002), 273-284. |
[21] |
S. I. Pohozaev and A. Tesei, Nonexistence of local solutions to semilinear partial differential inequalities, Ann. Inst. H. Poincaré Anal. Non Linéaire, 21 (2004), 487-502.
doi: 10.1016/j.anihpc.2003.06.002. |
show all references
References:
[1] |
E. Galakhov, Some nonexistence results for quasilinear PDE's, Commun. Pure Appl. Anal., 6 (2007), 141-161.
doi: 10.1002/cpa.3160390306. |
[2] |
E. Mitidieri and S. I. Pohozaev, Absence of positive solutions for quasilinear elliptic problems in $\mathbb{R}^N2$, Proc. Steklov Inst. Math., 227 (1999), 186-216. |
[3] |
E. Mitidieri and S. I. Pohozaev, Nonexistence of weak solutions for some degenerate elliptic and parabolic problems on $R^n$, J. Evol. Equ., 1 (2001), 189-220.
doi: 10.1007/PL00001368. |
[4] |
E. Mitidieri and S. I. Pohozaev, A priori estimates and the absence of solutions of nonlinear partial differential equations and inequalities, Proc. Steklov Inst. Math., 234 (2001), 1-362. |
[5] |
E. Mitidieri and S. I. Pohozaev, Towards a unified approach to nonexistence of solutions for a class of differential inequalities, Milan J. Math., 72 (2004), 129-162.
doi: 10.1007/s00032-004-0032-7. |
[6] |
G. Karisti, On the absence of solutions of systems of quasilinear elliptic inequalities, Differ. Equs., 38 (2002), 375-383.
doi: 10.1023/A:1016061909813. |
[7] |
G. G. Laptev, On the absence of solutions to a class of singular semilinear differential inequalities, Proc. Steklov Inst. Math., 232 (2001), 216-228. |
[8] |
H. Brezis and X. Cabré, Some simple nonlinear PDE's without solutions, Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat., 1 (1998), 223-262. |
[9] |
J. Serrin and H. Zou, Cauchy-Liouville and universal boundedness theorems for quasilinear elliptic equations and inequalities, Acta Math., 189 (2002), 79-142.
doi: 10.1007/BF02392645. |
[10] |
J. Serrin, Entire solutions of quasilinear elliptic equations, J. Math. Anal. Appl., 352 (2009), 3-14.
doi: 10.1016/j.jmaa.2008.10.036. |
[11] |
L. D'Ambrosio, Liouville theorems for anisotropic quasilinear inequalities, Nonlinear Anal., 70 (2009), 2855-2869.
doi: 10.1016/j.na.2008.12.028. |
[12] |
L. D'Ambrosio and E. Mitidieri, Nonnegative solutions of some quasilinear elliptic inequalities and applications, Mat. Sb., 201 (2010), 1-20.
doi: 10.1070/SM2010v201n06ABEH004094. |
[13] |
L. D'Ambrosio and E. Mitidieri, A priori estimates, positivity results, and nonexistence theorems for quasilinear degenerate elliptic inequalities, Adv. Math., 224 (2010), 967-1020.
doi: 10.1016/j.aim.2009.12.017. |
[14] |
M. F. Bidaut-Véron and S. Pohozaev, Nonexistence results and estimates for some nonlinear elliptic problems, J. Anal. Math., 84 (2001), 1-49.
doi: 10.1007/BF02788105. |
[15] |
R. Filippucci, Nonexistence of positive weak solutions of elliptic inequalities, Nonlinear Anal., 70 (2009), 2903-2916.
doi: 10.1016/j.na.2008.12.018. |
[16] |
R. Filippucci, P. Pucci and M. Rigoli, Non-existence of entire solutions of degenerate elliptic inequalities with weights, Arch. Ration. Mech. Anal., 188 (2008), 155-179.
doi: 10.1017/s00205-007-0081-5. |
[17] |
R. Filippucci, P. Pucci and M. Rigoli, On weak solutions of nonlinear weighted $p$-Laplacian elliptic inequalities, Nonlinear Anal., 70 (2009), 3008-3019.
doi: 10.1016/j.na.2008.12.031. |
[18] |
R. Filippucci, P. Pucci and M. Rigoli, On entire solutions of degenerate elliptic differential inequalities with nonlinear gradient terms, J. Math. Anal. Appl., 356 (2009), 689-697.
doi: 10.1016/j.jmaa.2009.03.050. |
[19] |
R. Filippucci, P. Pucci and M. Rigoli, Nonlinear weighted $p$-Laplacian elliptic inequalities with gradient terms, Commun. Contemp. Math., 12 (2010), 501-535.
doi: 10.1142/S0219199710003841. |
[20] |
S. I. Pohozaev, A general approach to the theory of the nonexistence of global solutions of nonlinear partial differential equations and inequalities, Proc. Steklov Inst. Math., 236 (2002), 273-284. |
[21] |
S. I. Pohozaev and A. Tesei, Nonexistence of local solutions to semilinear partial differential inequalities, Ann. Inst. H. Poincaré Anal. Non Linéaire, 21 (2004), 487-502.
doi: 10.1016/j.anihpc.2003.06.002. |
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