Existence and asymptotic behaviour of positive solutions for semilinear polyharmonic coupled systems

References

• Karamata J. Sur un mode de croissance régulière des fonctions [About a regular growth of functions]. Mathematica(Cluj). 1930;4:38–53.
   Google Scholar
• Cîrstea F, Rădulescu V. Uniqueness of the blow-up boundary solution of logistic equations with absorption. C R Acad Sci Paris Ser. 2002;I(335):447–452.
   Web of Science ®Google Scholar
• Cîrstea F, Rădulescu V. Asymptotics for the blow-up boundary solution of logistic equations with absorption. C R Acad Sci Paris Ser. 2003;I(336):231–236.
   Web of Science ®Google Scholar
• Cîrstea F, Rădulescu V. Nonlinear problems with boundary blow-up: a Karamata regular variation theory approch. Asympt Anal. 2006;46:275–298.
   Web of Science ®Google Scholar
• Cîrstea F, Rădulescu V. Boundary blow-up in nonlinear elliptic equations of Bieberbach--Rademacher type. Trans Am Math Soc. 2007;359:3275–3286.
   Web of Science ®Google Scholar
• Busca J, Manàsevish R. A Liouville-type theorem for Lane--Emden system. Indiana Univ Math. 2002;51:37–51.
   Web of Science ®Google Scholar
• Chemmam R, Mâagli H, Masmoudi S, et al. Combined effects in nonlinear singular elliptic problems in a bounded domain. Adv Nonlinear Anal. 2012;1:301–318.
   Web of Science ®Google Scholar
• Giacomoni J, Hernandez J, Sauvy P. Quasilinear and singular elliptic systems. Adv Nonlinear Anal. 2012;2:1–42.
   Web of Science ®Google Scholar
• Mâagli H. Asymptotic behavior of positive solutions of a semilinear Dirichlet problems. Nonlinear Anal. 2011;74:2941–2947.
   Web of Science ®Google Scholar
• Mâagli H, Ben Othman S, Chemmam R. Asymptotic behavior of positive large solutions of semilinear Dirichlet problems. Electron J Qual Theory Differ Equ. 2013;57:1–13.
   Google Scholar
• Mâagli H, Ben Othman S, Dridi S. Existence and asymptotic behavior of ground state solutions of semilinear elliptic system. Adv Nonlinear Anal. 2016:2191–9496. DOI: 10.1515/anona-2015-0157.
   Web of Science ®Google Scholar
• Mâagli H, Turki S, Zine El Abidine Z. Asymptotic behavior of positive solutions of a semilinear Dirichlet problem outside the unit ball. Electron J Differ Equ. 2013;95:1–14.
   Google Scholar
• Masmoudi S, Zermani S. Existence and asymptotic behavior of solutions to nonlinear radial p-Laplacian equations. Electron J Differ Equ. 2015;171:1–12.
   Google Scholar
• Rădulesc V. Singular phenomena in nonlinear elliptic problems: from blow-up boundary solutions to equations with singular nonlinearities. Vol. 4, In: Chipot M, editor. Handbook of differential equations: stationary partial differential equations. Amsterdam: North-Holland Elsevier Science; 2007. p. 483–591.
   Google Scholar
• Rădulesc V. Qualitative analysis of nonlinear elliptic partial differential equations: monotonicity, analytic and variational methods. New York (NY): Hindawi Publishing Corporation; 2008. (Contemporary Mathematics and its Applications).
   Google Scholar
• Bachar I, Mâagli H, Masmoudi S, et al. Estimates for the Green function and singular solutions for polyharmonic nonlinear equation. Abstract Appl Anal. 2003;2003:715–741.
   Google Scholar
• Bachar I, Zribi M. Existence results for some polyharmonic problems in the half-space. J Math Anal Appl. 2006;322:610–620.
   Web of Science ®Google Scholar
• Ben Othman S. On a singular sublinear polyharmonic problem. Abstract Appl Anal. 2006;2006:1–14.
   Google Scholar
• Dhifli A. Zine El Abidine Z. Asymptotic behavior of positive solutions of a semilinear polyharmonic problem in the unit ball. Nonlinear Anal. 2012;75:625–636.
   Web of Science ®Google Scholar
• Goyal S, Sreenadh K. The Nehari manifold for a quasilinear polyharmonic equation with exponential nonlinearities and a sign-changing weight function. Adv Nonlinear Anal. 2015;4:177–200.
   Web of Science ®Google Scholar
• Zine El Abidine Z. Combined effects in a semilinear polyharmonic problem in the unit ball. Acta Math Sci. 2014;34B:1404–1416.
   Google Scholar
• Gontara S, Zine El Abidine Z. Existence of positive bounded solutions for some nonlinear polyharmonic elliptic systems. Electron J Differ Equ. 2010;113:1–18.
   Google Scholar
• Turki S. Existence of positive continuous solutions for some nonlinear polyharmonic systems outside the unit ball. Electron J Differ Equ. 2011;81:1–13.
   Google Scholar
• Zine El Abidine Z. On the existence of positive continuous solutions for some polyharmonic elliptic systems on the half space. Opuscula Math. 2012;32:91–113.
   Google Scholar
• Alsaedi R, Mâagli H, Zeddini N. Positive solutions for some competitive elliptic systems. Math Slovaca. 2014;64:61–72.
   Web of Science ®Google Scholar
• Barile S, Salvatore A. Existence and multiplicity results for some Lane--Emden elliptic systems: subquadratic case. Adv Nonlinear Anal. 2015;4:25–35.
   Web of Science ®Google Scholar
• Chaieb M, Dhifli A, Zermani S. Existence and asymptotic behavior of positive solutions of a semilinear elliptic system in a bounded domain. Opuscula Math. 2016;36:315–336.
   Web of Science ®Google Scholar
• Clément Ph, Fleckinger J, Mitidieri E, et al. Existence of positive solutions for a nonvariational quasilinear elliptic system. J Differ Equ. 2000;166:455–477.
   Web of Science ®Google Scholar
• Dalmasso R. Existence and uniqueness of positive solutions of semilinear elliptic systems. Nonlinear Anal. 2000;39:559–568.
   Web of Science ®Google Scholar
• De Figueiredo DG. Semilinear elliptic systems. In: Ambrosetti A, Chang KC, Ekeland I, editors. Proceedings of the Second School on Nonlinear Functional Analysis and Applications to Differential Equations; 1997; ICTP Trieste; Trieste: World Scientific Publishing Company; 1998. p. 122–152.
   Google Scholar
• De Figueiredo DG, Felmer P. A Liouville-type theorem for elliptic systems. Ann Sc Norm Super Pisa CI Sci. 1994;21:387–397.
   Google Scholar
• De Figueiredo DG, Sirakov B. Liouville type theorems, monotonicity results and a priori bounds for positive solutions of elliptic systems. Math Ann. 2005;333:231–260.
   Web of Science ®Google Scholar
• Ghanmi A, Mâagli H, Rădulescu V, et al. Large and bounded solutions for a class of nonlinear Schödinger stationnary systems. Ana Appl. 2009;7:391–404.
   Web of Science ®Google Scholar
• Ghergu M. Lane--Emden systems with negative exponents. J Funct Anal. 2010;528:3259–3318.
   Google Scholar
• Ghergu M. Steady-state solutions for Gierer--Meinhardt type systems with Dirichlet boundary conditions. Trans Am Math Soc. 2009;361:3953–3976.
   Web of Science ®Google Scholar
• Ghergu M, Rădulescu V. On a class of singular Gierer--Meinhardt systems arising in morphogenesis. C R Math Acad Sci Paris. 2007;344:163–168.
   Web of Science ®Google Scholar
• Ghergu M, Rădulescu V. A singular Gierer--Meinhardt system with different source terms. Proc R Soc Edinburgh Sect. 2008;A138:1215–1234.
   Web of Science ®Google Scholar
• Melián JG, Rossi JD. Boundary blow-up solutions to elliptic systems of competitive type. J Differ Equ. 2004;206:156–181.
   Web of Science ®Google Scholar
• Melián JG, Rossi JD, Sabine De Lis JC. An elliptic system with bifurcation parameters on the boundary conditions. J Differ Equ. 2009;247:779–810.
   Web of Science ®Google Scholar
• Zhang Z. Positive solutions of Lane--Emden systems with negative exponents: Existence, boundary behavior and uniqueness. Nonlinear Anal. 2011;74:5544–5553.
   Web of Science ®Google Scholar
• Boggio T. Sulle funzioni di Green d’ordine m. Rend Circ Math Palermo. 1905;20:97–135.
   Google Scholar
• Marić V. Regular variation and differential equations. Berlin: Springer; 2000. (Lecture Notes in Mathematics; 1726).
   Google Scholar
• Seneta R. Regular varying functions. Berlin: Springer; 1976. (Lectures Notes in Mathematics; 508).
   Google Scholar