[1]

H. Amann,
On the existence of positive solutions of nonlinear elliptic boundary value problems,
Indiana Univ. Math. J. 21 (1971/72), 125–146.
CrossrefGoogle Scholar

[2]

A. Ambrosetti, H. Brezis and G. Cerami,
Combined effects of concave and convex nonlinearities in some elliptic problems,
J. Funct. Anal. 122 (1994), no. 2, 519–543.
CrossrefGoogle Scholar

[3]

D. Arcoya, L. Boccardo, T. Leonori and A. Porretta,
Some elliptic problems with singular natural growth lower order terms,
J. Differential Equations 249 (2010), no. 11, 2771–2795.
Web of ScienceCrossrefGoogle Scholar

[4]

D. Arcoya, J. Carmona, T. Leonori, P. J. Martínez-Aparicio, L. Orsina and F. Petitta,
Existence and nonexistence of solutions for singular quadratic quasilinear equations,
J. Differential Equations 246 (2009), no. 10, 4006–4042.
Web of ScienceCrossrefGoogle Scholar

[5]

D. Arcoya, J. Carmona and P. J. Martínez-Aparicio,
Bifurcation for quasilinear elliptic singular BVP,
Comm. Partial Differential Equations 36 (2011), no. 4, 670–692.
CrossrefGoogle Scholar

[6]

D. Arcoya and S. Segura de León,
Uniqueness of solutions for some elliptic equations with a quadratic gradient term,
ESAIM Control Optim. Calc. Var. 16 (2010), no. 2, 327–336.
CrossrefWeb of ScienceGoogle Scholar

[7]

C. Bandle and M. Marcus,
“Large” solutions of semilinear elliptic equations: Existence, uniqueness and asymptotic behaviour,
J. Anal. Math. 58 (1992), 9–24;
Festschrift on the occasion of the 70th birthday of Shmuel Agmon.
CrossrefGoogle Scholar

[8]

L. Boccardo,
Dirichlet problems with singular and gradient quadratic lower order terms,
ESAIM Control Optim. Calc. Var. 14 (2008), no. 3, 411–426.
Web of ScienceCrossrefGoogle Scholar

[9]

L. Boccardo and L. Orsina,
Semilinear elliptic equations with singular nonlinearities,
Calc. Var. Partial Differential Equations 37 (2010), no. 3–4, 363–380.
CrossrefWeb of ScienceGoogle Scholar

[10]

J. Carmona and T. Leonori,
A uniqueness result for a singular elliptic equation with gradient term,
Proc. Roy. Soc. Edinburgh Sect. A 148 (2018), no. 5, 983–994.
CrossrefWeb of ScienceGoogle Scholar

[11]

J. Carmona, T. Leonori, S. López-Martínez and P. J. Martínez-Aparicio,
Quasilinear elliptic problems with singular and homogeneous lower order terms,
Nonlinear Anal. 179 (2019), 105–130.
CrossrefWeb of ScienceGoogle Scholar

[12]

J. Carmona, P. J. Martínez-Aparicio and A. Suárez,
Existence and non-existence of positive solutions for nonlinear elliptic singular equations with natural growth,
Nonlinear Anal. 89 (2013), 157–169.
CrossrefWeb of ScienceGoogle Scholar

[13]

J. Carmona Tapia, A. Molino Salas and L. Moreno Mérida,
Existence of a continuum of solutions for a quasilinear elliptic singular problem,
J. Math. Anal. Appl. 436 (2016), no. 2, 1048–1062.
CrossrefWeb of ScienceGoogle Scholar

[14]

M. G. Crandall, P. H. Rabinowitz and L. Tartar,
On a Dirichlet problem with a singular nonlinearity,
Comm. Partial Differential Equations 2 (1977), no. 2, 193–222.
CrossrefGoogle Scholar

[15]

S. Cui,
Existence and nonexistence of positive solutions for singular semilinear elliptic boundary value problems,
Nonlinear Anal. 41 (2000), no. 1–2, 149–176.
CrossrefGoogle Scholar

[16]

Y. Du,
Order Structure and Topological Methods in Nonlinear Partial Differential Equations. Vol. 1. Maximum Principles and Applications,
Ser. Part. Diff. Equ. Appl. 2,
World Scientific, Hackensack, 2006.
Google Scholar

[17]

Y. Du and Q. Huang,
Blow-up solutions for a class of semilinear elliptic and parabolic equations,
SIAM J. Math. Anal. 31 (1999), no. 1, 1–18.
CrossrefGoogle Scholar

[18]

J. García-Melián,
Boundary behavior for large solutions to elliptic equations with singular weights,
Nonlinear Anal. 67 (2007), no. 3, 818–826.
CrossrefWeb of ScienceGoogle Scholar

[19]

M. Ghergu and V. D. Rădulescu,
Singular Elliptic Problems: Bifurcation and Asymptotic Analysis,
Oxford Lecture Ser. Math. Appl. 37,
Oxford University, Oxford, 2008.
Google Scholar

[20]

D. Giachetti, F. Petitta and S. S. de León,
Elliptic equations having a singular quadratic gradient term and a changing sign datum,
Commun. Pure Appl. Anal. 11 (2012), no. 5, 1875–1895.
Web of ScienceCrossrefGoogle Scholar

[21]

D. Giachetti, F. Petitta and S. Segura de León,
A priori estimates for elliptic problems with a strongly singular gradient term and a general datum,
Differential Integral Equations 26 (2013), no. 9–10, 913–948.
Google Scholar

[22]

D. Giachetti and S. Segura de León,
Quasilinear stationary problems with a quadratic gradient term having singularities,
J. Lond. Math. Soc. (2) 86 (2012), no. 2, 585–606.
CrossrefGoogle Scholar

[23]

J. B. Keller,
On solutions of $\mathrm{\Delta}u=f(u)$,
Comm. Pure Appl. Math. 10 (1957), 503–510.
Google Scholar

[24]

A. C. Lazer and P. J. McKenna,
On a singular nonlinear elliptic boundary-value problem,
Proc. Amer. Math. Soc. 111 (1991), no. 3, 721–730.
CrossrefGoogle Scholar

[25]

S. Leonardi,
Morrey estimates for some classes of elliptic equations with a lower order term,
Nonlinear Anal. 177 (2018), 611–627.
Web of ScienceCrossrefGoogle Scholar

[26]

J. López-Gómez,
Large solutions, metasolutions, and asymptotic behaviour of the regular positive solutions of sublinear parabolic problems,
Proceedings of the Conference on Nonlinear Differential Equations (Coral Gables 1999),
Electron. J. Differ. Equ. Conf. 5,
Southwest Texas State University, San Marcos (2000), 135–171.
Google Scholar

[27]

J. López-Gómez,
Optimal uniqueness theorems and exact blow-up rates of large solutions,
J. Differential Equations 224 (2006), no. 2, 385–439.
CrossrefGoogle Scholar

[28]

J. López-Gómez,
Metasolutions of Parabolic Equations in Population Dynamics,
CRC Press, Boca Raton, 2016.
Google Scholar

[29]

J. López-Gómez and L. Maire,
Uniqueness of large positive solutions,
Z. Angew. Math. Phys. 68 (2017), no. 4, Article ID 86.
Web of ScienceGoogle Scholar

[30]

M. Marcus and L. Véron,
Uniqueness and asymptotic behavior of solutions with boundary blow-up for a class of nonlinear elliptic equations,
Ann. Inst. H. Poincaré Anal. Non Linéaire 14 (1997), no. 2, 237–274.
CrossrefGoogle Scholar

[31]

M. Marcus and L. Véron,
Existence and uniqueness results for large solutions of general nonlinear elliptic equations,
J. Evol. Equ. 3 (2003), no. 4, 637–652.
CrossrefGoogle Scholar

[32]

F. Oliva and F. Petitta,
Finite and infinite energy solutions of singular elliptic problems: Existence and uniqueness,
J. Differential Equations 264 (2018), no. 1, 311–340.
CrossrefWeb of ScienceGoogle Scholar

[33]

R. Osserman,
On the inequality $\mathrm{\Delta}u\ge f(u)$,
Pacific J. Math. 7 (1957), 1641–1647.
Google Scholar

[34]

G. Porru and A. Vitolo,
Problems for elliptic singular equations with a quadratic gradient term,
J. Math. Anal. Appl. 334 (2007), no. 1, 467–486.
CrossrefWeb of ScienceGoogle Scholar

[35]

J. Shi and M. Yao,
On a singular nonlinear semilinear elliptic problem,
Proc. Roy. Soc. Edinburgh Sect. A 128 (1998), no. 6, 1389–1401.
CrossrefGoogle Scholar

[36]

S. Tao and Z. Zhang,
On the existence of explosive solutions for semilinear elliptic problems,
Nonlinear Anal. 48 (2002), no. 7, 1043–1050.
CrossrefGoogle Scholar

[37]

L. Véron,
Semilinear elliptic equations with uniform blow-up on the boundary,
J. Anal. Math. 59 (1992), 231–250;
Festschrift on the occasion of the 70th birthday of Shmuel Agmon.
CrossrefGoogle Scholar

[38]

L. Véron,
Large solutions of elliptic equations with strong absorption,
Elliptic and Parabolic Problems,
Progr. Nonlinear Differential Equations Appl. 63,
Birkhäuser, Basel (2005), 453–464.
Google Scholar

[39]

N. Zeddini, R. Alsaedi and H. Mâagli,
Exact boundary behavior of the unique positive solution to some singular elliptic problems,
Nonlinear Anal. 89 (2013), 146–156.
CrossrefWeb of ScienceGoogle Scholar

[40]

Z. Zhang,
Boundary behavior of solutions to some singular elliptic boundary value problems,
Nonlinear Anal. 69 (2008), no. 7, 2293–2302.
CrossrefWeb of ScienceGoogle Scholar

[41]

Z. Zhang,
Boundary behavior of large solutions for semilinear elliptic equations with weights,
Asymptot. Anal. 96 (2016), no. 3–4, 309–329.
CrossrefGoogle Scholar

[42]

Z. Zhang, B. Li and X. Li,
The exact boundary behavior of solutions to singular nonlinear Lane–Emden–Fowler type boundary value problems,
Nonlinear Anal. Real World Appl. 21 (2015), 34–52.
CrossrefWeb of ScienceGoogle Scholar

[43]

Z. Zhang, X. Li and Y. Zhao,
Boundary behavior of solutions to singular boundary value problems for nonlinear elliptic equations,
Adv. Nonlinear Stud. 10 (2010), no. 2, 249–261.
Google Scholar

[44]

W. Zhou,
Existence and multiplicity of weak solutions to a singular semilinear elliptic equation,
J. Math. Anal. Appl. 346 (2008), no. 1, 107–119.
Web of ScienceCrossrefGoogle Scholar

[45]

W. Zhou, X. Wei and X. Qin,
Nonexistence of solutions for singular elliptic equations with a quadratic gradient term,
Nonlinear Anal. 75 (2012), no. 15, 5845–5850.
CrossrefWeb of ScienceGoogle Scholar

## Comments (0)

General note:By using the comment function on degruyter.com you agree to our Privacy Statement. A respectful treatment of one another is important to us. Therefore we would like to draw your attention to our House Rules.