Large solutions for a class of nonlinear elliptic equations with gradient terms

Advanced Nonlinear Studies

Volumn 7, Issue 2, 2007, Pages 237-269

  Leonori, Tommaso ^a  

^a UNIVERSITY OF ROME TOR VERGATA   (Italy)

Author keywords

Gradient terms; Large solutions; Nonlinear elliptic equations

Indexed keywords

EID: 34247277686     PISSN: 15361365     EISSN: None     Source Type: Journal    
DOI: 10.1515/ans-2007-0204     Document Type: Article

References (29)

1. C. Bandle, M. Essen, On the solutions of quasilinear elliptic problems with boundary blow-up. Partial differential equations of elliptic type (Cortona, 1992), 93-111, Sympos. Math., XXXV, Cambridge Univ. Press, Cambridge, 1994.
2. C. Bandle, E. Giarrusso, Boundary blow-up for semilinear elliptic equations with nonlinear gradient terms, Adv. Diff. Equat. 1 (1996), 133-150.
3. C. Bandle, M. Marcus, Large solutions of semilinear elliptic equations: existence, uniqueness and asymptotic behavior, J. Anal. Math. 58 (1992), 9-24.
4. C. Bandle, M. Marcus, Dependence of blow-up rate of large solutions of semilinear elliptic equations on the curvature of the boundary, Complex Var. Theory Appl. 49 (2004), 555-570.
5. P. Bénilan, L. Boccardo, T. Gallouët, R. Gariepy, M. Pierre, J. L. Vazquez, An L1- theory of existence and uniqueness of nonlinear elliptic equations, Ann. Scuola Norm. Sup. Pisa Cl. Sci., 22 (1995), 241-273.
6. A. Bensoussan, L. Boccardo, F. Murat, On a nonlinear P.D.E. having natural growth terms and unbounded solutions, Ann. Inst. H. Poincare Anal. Non Lineaire, 5 (1988), 347-364.
7. L. Boccardo, I. Diaz, D. Giachetti, F. Murat, Existence of a solution for a weaker form of a nonlinear elliptic equation, Recent advances in nonlinear elliptic and parabolic problems (Nancy, 1988), Pitman Res. Notes Math. Ser. 208, 229-246, Longman, 1989.
8. L. Boccardo, T. Gallouët, Nonlinear elliptic and parabolic equations involving measure data, J. Funct. Anal., 87 (1989), 149-169.
9. 1 data, Nonlinear Anal. T.M.A., 19 (1992), 573-579.
10. L. Boccardo, T. Gallouët, L. Orsina, Existence and nonexistence of solutions for some nonlinear elliptic equations, Journal D'Analyse Mathematique, 73 (1997), 203-223.
11. N without growth conditions on the data, J. Diff, Eq. 105 (1993), 334-363.
12. ∞ estimate for some nonlinear elliptic partial differential equations and application to an existence result, SIAM J. Math. Anal. 23 (1992), n. 2, 326-333.
13. N without condition at infinity, Appl. Math. Optim. 12 (1984), n. 3, 271-282.
14. G. Dal Maso, F. Murat, L. Orsina, A. Prignet, Renormalized solutions of elliptic equations with general measure data, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 28 (1999), 741-808.
15. M. Ghergu, V. Radulescu, On a class of sublinear singular elliptic problems with convection term, J. Math, Anal. Appl. 311 (2005), no. 2, 635-646.
16. J.B. Keller, On solutions of Δu = f(u), Commun. Pure Appl. Math. 10 (1957), 503-510.
17. J.-M. Lasry, P.-L. Lions, Nonlinear elliptic equations with singular boundary conditions and stochastic control with state constraints. I. The model problem, Math. Ann. 283 (1989), n. 4, 583-630.
18. N with "absorbing" zero order terms, Adv. Differential Equations 5 (2000), n. 4-6, 681-722.
19. J. Leray, J.L. Lions, Quelques résultats de Višik sur les problèmes elliptiques non linéaires par les méthodes de Minty-Browder, Bull. Soc. Math. France, 93 (1965), 97-107.
20. P.-L. Lions, F. Murat, Renormalized solutions for nonlinear elliptic equations, unpublished paper.
21. M. Marcus, L. Veron, Uniqueness and asymptotic behaviour of solutions with boundary blow-up for a class of nonlinear elliptic equations, Ann. Inst. H. Poincaré 14 (1997), 237-274.
22. M. Marcus, L. Veron, Existence and uniqueness results for large solutions of general nonlinear elliptic equations. Dedicated to Philippe Bnilan. J. Evol. Equ. 3 (2003), no. 4, 637-652.
23. R. Osserman, On the inequality Δu ≥ f(u), Pacific J. Math. 7 (1957), 1641-1647.
24. A. Porretta, Some remarks on the regularity of solutions for a class of elliptic equations with measure data, Houston Journ. of Math. 26 (2000), 183-213.
25. A. Porretta, Some uniqueness results for elliptic equations without condition at infinity Commun. Contemp. Math. 5 (2003), no. 5, 705-717.
26. A. Porretta, Local estimates and large solutions for some elliptic equation with absorption, Adv. Diff. Eq. 9, (2004), 329-351.
27. G. Stampacchia, Le problème de Dirichlet pour les équations elliptiques du seconde ordre à coefficientes discontinus, Ann. Inst. Fourier (Grenoble), 15 (1965), 189-258.
28. L. Veron, Semilinear elliptic equations with uniform blow-up on the boundary, J. Analyse Math. 59 (1992), 231-250.
29. Z. Zhang, The asymptotic behaviour of solutions with boundary blow-up for semilinear elliptic equations with nonlinear gradient terms, Nonlinear Anal. 62 (2005) 1137-1148.