Dirichlet problems with singular and gradient quadratic lower order terms

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1. D. Arcoya, S. Barile and P.J. Martinez-Aparicio, Singular quasilinear equations with quadratic growth in the gradient without sign condition. Preprint.  
2. D. Arcoya and P.J. Martinez-Aparicio, Quasilinear equations with natural growth Rev. Mat. Iberoamericana (to appear). 
3. D. Arcoya, J. Carmona, T. Leonori, P.J. Martínez, L. Orsina and F. Petitta, Quadratic quasilinear equations with general singularities. Preprint.  
4. A. Bensoussan, L. Boccardo and F. Murat, On a nonlinear partial differential equation having natural growth terms and unbounded solution. Ann. Inst. H. Poincaré Anal. Non Linéaire5 (1988) 347–364.  
5. L. Boccardo, Some nonlinear Dirichlet problems in $L^1$ involving lower order terms in divergence form, in Progress in elliptic and parabolic partial differential equations (Capri, 1994), Pitman Res. Notes Math. Ser.350, Longman, Harlow (1996) 43–57.  
6. L. Boccardo, Positive solutions for some quasilinear elliptic equations with natural growths. Atti Accad. Naz. Lincei11 (2000) 31–39.  
7. L. Boccardo, Hardy potential and quasi-linear elliptic problems having natural growth terms, in Proceedings of the Conference held in Gaeta on the occasion of the 60th birthday of Haim Brezis, Progr. Nonlinear Differential Equations Appl.63, Birkhauser, Basel (2005) 67–82.  
8. L. Boccardo and T. Gallouët, Nonlinear elliptic and parabolic equations involving measure data. J. Funct. Anal.87 (1989) 149–169.  
9. L. Boccardo and T. Gallouët, Strongly nonlinear elliptic equations having natural growth terms and L1 data. Nonlinear Anal.19 (1992) 573–579.  
10. L. Boccardo, T. Gallouët and L. Orsina, Existence and nonexistence of solutions for some nonlinear elliptic equations. J. Anal. Math.73 (1997) 203–223.  
11. L. Boccardo and D. Giachetti, Existence results via regularity for some nonlinear elliptic problems. Comm. Partial Diff. Eq.14 (1989) 663–680.  
12. L. Boccardo and F. Murat, Almost everywhere convergence of the gradients of solutions to elliptic and parabolic equations. Nonlinear Anal. TMA19 (1992) 581–597.  
13. L. Boccardo, F. Murat and J.-P. Puel, Existence de solutions non bornées pour certaines équations quasi-linéaires. Portugaliae Math.41 (1982) 507–534.  
14. L. Boccardo, F. Murat and J.-P. Puel, Résultats d'existence pour certains problèmes elliptiques quasi linéaires. Ann. Sc. Norm. Sup. Pisa11 (1984) 213–235.  
15. L. Boccardo, F. Murat and J.-P. Puel, Existence of bounded solutions for nonlinear elliptic unilateral problems. Ann. Mat. Pura Appl.152 (1988) 183–196.  
16. L. Boccardo, F. Murat and J.-P. Puel, $L^{\infty }$-estimates for some nonlinear partial differential equations and application to an existence result. SIAM J. Math. Anal.23 (1992) 326–333.  
17. H. Brezis and L. Nirenberg, Removable singularities for nonlinear elliptic equations. Topol. Methods Nonlinear Anal.9 (1997) 201–219.  
18. M.G. Crandall, P.H. Rabinowitz and L. Tartar, On a Dirichlet problem with a singular nonlinearity. Comm. Partial Diff. Eq.2 (1977) 193–222.  
19. A. Dall'Aglio, D. Giachetti and J.-P. Puel, Nonlinear elliptic equations with natural growth in general domains. Ann. Mat. Pura Appl.181 (2002) 407–426.  
20. A. Dall'Aglio, V. De Cicco, D. Giachetti and J.-P. Puel, Existence of bounded solutions for nonlinear elliptic equations in unbounded domains. NoDEA11 (2004) 431–450.  
21. T. Del Vecchio, Strongly nonlinear problems with Hamiltonian having natural growth. Houston J. Math.16 (1990) 7–24.  
22. D. Giachetti and F. Murat, Personal communication.  
23. J.B. Keller, On solutions of $\Delta u=f\left(u\right)$. Commun. Pure Appl. Math.10 (1957) 503–510.  
24. A.C. Lazer and P.J. McKenna, On a singular nonlinear elliptic boundary-value problem. Proc. Amer. Math. Soc.111 (1991) 721–730.  
25. T. Leonori, Large solutions for a class of nonlinear elliptic equations with gradient terms. Adv. Nonlinear Stud.7 (2007) 237–269.  
26. R. Osserman, On the inequality $\Delta u\ge f\left(u\right)$. Pacific J. Math.7 (1957) 1641–1647.  
27. A. Porretta, Existence for elliptic equations in L1 having lower order terms with natural growth. Portugaliae Math.57 (2000) 179–190.  
28. A. Porretta, A local estimates and large solutions for some elliptic equations with absorption. Adv. Differential Equations9 (2004) 329–351.  
29. A. Porretta and S. Segura de Leon, Nonlinear elliptic equations having a gradient term with natural growth. J. Math. Pures Appl.85 (2006) 465–492.  
30. J.-P. Puel, Existence, comportement à l'infini et stabilité dans certains problèmes quasilinéaires elliptiques et paraboliques d'ordre 2. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4)3 (1976) 89–119.  
31. G. Stampacchia, Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus. Ann. Inst. Fourier (Grenoble)15 (1965) 189–258.  
32. N.S. Trudinger, On Harnack type inequalities and their application to quasilinear elliptic equations. Comm. Pure Appl. Math.20 (1967) 721–747.  
33. J.L. Vazquez, The Porous Medium Equation: Mathematical Theory, Oxford Mathematical Monographs. Oxford University Press, Oxford (2007).  

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