Existence and a priori estimates for semilinear elliptic systems of Hardy type
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Abstract
We study semilinear elliptic systems of Hardy type on bounded domains. We look for conditions guaranteeing the existence and uniform boundedness of very weak solutions satisfying homogeneous Dirichlet boundary conditions.
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Pačuta, J.
(2014).
Existence and a priori estimates for semilinear elliptic systems of Hardy type.
Acta Mathematica Universitatis Comenianae, 83(2), 321-330.
Retrieved from http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/26/95
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References
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[10] Phan Q.H. : Liouville-type theorems and bounds of solutions for Hardy-Henon elliptic systems, Adv. Dierential Equations 17 (2012), 605-634.
[11] Quittner P., Souplet Ph. : A priori estimates and existence for elliptic systems via bootstrap in weighted Lebesgue spaces, Arch. Rational Mech. Anal. 174 (2004), 49-81.
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[13] Souplet Ph. : Optimal regularity conditions for elliptic problems via Lp ()-spaces, Duke Math. J. 127 (2005), 175-192. 12 (1960), 21-37.
[2] Bidaut-Veron M.F., Giacomini H. : A new dynamical approach of Emden-Fowler equations and systems, Adv. Dierential Equations 15 (2010), 1033-1082.
[3] Bidaut-Veron M.F., Yarur C. : Semilinear elliptic equations and systems with measure data: existence and a priori estimates , Adv. Dierential Equations 7 (2002), 257-296.
[4] Calanchi M., Ruf B. : Radial and non radial solutions for Hardy-Henon type elliptic systems, Calc. Var. 38 (2010), 111-133.
[5] De Figueiredo D.G., Peral I., Rossi J.D. : The critical hyperbola for a Hamiltonian elliptic system with weights, Ann. Mat. Pura Appl. 187 (2008), 531-545.
[6] Del Pino M., Musso M., Pacard F. : Boundary singularities for weak solutions of semilinear elliptic problems, J. Funct. Anal. 253 (2007), 241-272.
[7] Fazly M. : Liouville type theorems for stable solutions of certain elliptic systems, Advanced Nonlinear Studies 12 (2012), 1-17.
[8] Gilbarg D., Trudinger N.S. : Elliptic partial dierential equations of second order, Springer, Berlin, (1998).
[9] Liu F., Yang J. : Nontrivial solutions of Hardy-Henon type elliptic systems, Acta Math. Sci. Ser. B Engl. Ed. 27 (2007), 673-688.
[10] Phan Q.H. : Liouville-type theorems and bounds of solutions for Hardy-Henon elliptic systems, Adv. Dierential Equations 17 (2012), 605-634.
[11] Quittner P., Souplet Ph. : A priori estimates and existence for elliptic systems via bootstrap in weighted Lebesgue spaces, Arch. Rational Mech. Anal. 174 (2004), 49-81.
[12] Quittner P., Souplet Ph. : Superlinear Parabolic Problems, Birkhauser (2007).
[13] Souplet Ph. : Optimal regularity conditions for elliptic problems via Lp ()-spaces, Duke Math. J. 127 (2005), 175-192. 12 (1960), 21-37.