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Applicable Analysis
An International Journal
Volume 98, 2019 - Issue 7
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Articles

On the existence of positive solutions to semilinear elliptic systems involving gradient term

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Pages 1289-1306 | Received 01 Dec 2017, Accepted 09 Dec 2017, Published online: 09 Jan 2018

References

  • Clain S , Rappaz J , Swierkosz M , Touzani R . Numerical modeling of induction heating for two dimentional geometrie. Math Models Methods Appl Sci. 1993;3(6):805–822.
  • Déaz JI , Lazzo M , Schmidt PG . Large solutions for a system of elliptic equation arising from fluid dynamics. SIAM J Math Anal. 2005;37:490–513.
  • Attar A , Bentifour R . Nonlinear elliptic system involving gradient term and reaction potential. Electron J Differ Equ. 2017;2017(113):1–10.
  • Boccardo L , Orsina L , Porretta A . Existence of finite energy solutions for elliptic systems with L1 –value nonlinearities. Math Models Methods Appl Sci. 2008;18(5):669–687.
  • Boccardo L , Orsina L , Puel J-P . A quasilinear elliptic system with natural growth terms. Ann Matematica. 2015;194(3):1733–1750.
  • Gazzola F , Grunau HC , Sweers G . Polyharmonic boundary value problems. Positivity preserving and nonlinear higher order elliptic equations in bounded domains. Lecture notes in mathematics 1991. Berlin: Springer-Verlag; 2010.
  • Escudero C , Peral I . Some fourth order nonlinear elliptic problems related to epitaxial growth. J Differ Equ. 2013;254:2515–2531.
  • Leray J , Lions J-L . Quelques résultats de Višik sur les problèmes elliptiques non linéaires par les méthodes de Minty-Browder. Bull Soc Math France. 1965;93:97–107.
  • Boccardo L , Murat F , Puel J-P . Existence des solutions non bornées pour certaines équations quasi-linéaires. Portugal Math. 1982;41:507–534.
  • Boccardo L , Gallouët T , Murat F . A unified representation of two existence results for problems with natural growth. Res Notes Math. 1993;296:127–137.
  • Cho K , Choe HJ . Nonlinear degenerate elliptic partial differential equations with critical growth conditions on the gradient. Proc AMS. 1995;123(12):3789–3796.
  • Ferone V , Murat F . Quasilinear problems having quadratic growth in the gradient: an existence result when the source term is small, Equations aux dérivées partielles et applications. Ed. Sci. Méd. Paris: Gauthier-Villars, Elsevier; 1998, 497–515.
  • Barles G , Porretta A . Uniqueness for unbounded solutions to stationary viscous Hamilton-Jacobi equations. Ann Sc Norm Super Pisa Cl Sci. 2006;5(1):107–136.
  • Grenon N , Trombetti C . Existence results for a class of nonlinear elliptic problems with p-growth in the gradient. Nonlinear Anal. 2003;52(3):931–942.
  • Lions P-L . Generalized solutions of Hamilton-Jacobi Equations. Pitman Res Notes Math. 1982;62.
  • Alaa NE , Pierre M . Weak solutions of some quasilinear elliptic equations with data measures. SIAM J Math Anal. 1993;24:23–35.
  • Grenon N , Murat F , Porretta A . Existence and a priori estimate for elliptic problems with subquadratic gradient dependent terms. C R Acad Sci Paris Ser I. 2006;342:23–28.
  • Hansson K , Maz’ya VG , Verbitsky IE . Criteria of solvability for multidimensional Riccati equations. Ark Mat. 1999;37:87–120.
  • Phuc NC . Morrey global bounds and qusilinear Riccarti type equation bellow the natural exponent. J Math Pures Appl. 2014;102:99–123.
  • Baras P , Pierre M . Critére d’existence des solutions positives pour des équations semi-linéaires non monotones. Ann IHP. 1985;2(3):185–212.
  • Baras P , Pierre M . Singularités éliminables pour des équations semi-linéaires. Ann Inst Fourier. 1984;34(1):185–206.
  • Brézis H . Functional analysis. Sobolev spaces and partial differential equations. New York (NY): Universitext, Springer; 2011.
  • Boccardo L , Croce G . Elliptic partial differential equations: existence and regularity of distributional solutions. Stud Math. 2014;55. De Gruyter.

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