Lane–Emden systems with negative exponents

Journal of Functional Analysis - Tập 258 Số 10 - Trang 3295-3318 - 2010
Marius Ghergu1
1School of Mathematical Sciences, University College Dublin, Belfield, Dublin 4, Ireland

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Tài liệu tham khảo

Busca, 2002, A Liouville-type theorem for Lane–Emden system, Indiana Univ. Math. J., 51, 37

Chandrasekhar, 1967

Clément, 2000, Existence of positive solutions for a nonvariational quasilinear elliptic system, J. Differential Equations, 166, 455, 10.1006/jdeq.2000.3805

Dupaigne, 2007, Lane–Emden–Fowler equations with convection and singular potential, J. Math. Pures Appl., 87, 563, 10.1016/j.matpur.2007.03.002

Emden, 1907

Felmer, 1994, A Liouville-type theorem for elliptic systems, Ann. Sc. Norm. Super. Pisa, 21, 387

de Figueiredo, 2005, Liouville type theorems, monotonicity results and a priori bounds for positive solutions of elliptic systems, Math. Ann., 333, 231, 10.1007/s00208-005-0639-1

Fowler, 1931, Further studies of Emden's and similar differential equations, Q. J. Math. (Oxford Ser.), 2, 259, 10.1093/qmath/os-2.1.259

Hernández, 2008, Positive solutions for singular semilinear elliptic systems, Adv. Differential Equations, 13, 857, 10.57262/ade/1355867322

Ghergu, 2009, Steady-state solutions for Gierer–Meinhardt type systems with Dirichlet boundary condition, Trans. Amer. Math. Soc., 361, 3953, 10.1090/S0002-9947-09-04670-4

Ghergu, 2007, On a class of singular Gierer–Meinhardt systems arising in morphogenesis, C. R. Math. Acad. Sci. Paris, 344, 163, 10.1016/j.crma.2006.12.008

Ghergu, 2008, A singular Gierer–Meinhardt system with different source terms, Proc. Roy. Soc. Edinburgh Sect. A, 138, 1215, 10.1017/S0308210507000637

Ghergu, 2008, Singular Elliptic Equations: Bifurcation and Asymptotic Analysis, vol. 37

Gui, 1993, Regularity of an elliptic problem with a singular nonlinearity, Proc. Roy. Soc. Edinburgh Sect. A, 123, 1021, 10.1017/S030821050002970X

Lane, 1869, On the theoretical temperature of the sun under hypothesis of a gaseous mass maintaining its volume by its internal heat and depending on the laws of gases known to terrestrial experiment, Amer. J. Sci., 50, 57

Naito, 2006, Existence of nonoscillatory solutions to second-order elliptic systems of Emden–Fowler type, Indiana Univ. Math. J., 55, 317, 10.1512/iumj.2006.55.2610

Protter, 1967

Quittner, 2004, A priori estimates and existence for elliptic systems via bootstrap in weighted Lebesgue spaces, Arch. Ration. Mech. Anal., 174, 49, 10.1007/s00205-004-0323-8

Reichel, 2000, Non-existence results for semilinear cooperative elliptic systems via moving spheres, J. Differential Equations, 161, 219, 10.1006/jdeq.1999.3700

Serrin, 1998, Existence of positive solutions of the Lane–Emden system, Atti Semin. Mat. Univ. Modena, XLVI, 369

Serrin, 1996, Non-existence of positive solutions of Lane–Emden systems, Differential Integral Equations, 9, 635, 10.57262/die/1367969879

Souplet, 2009, The proof of the Lane–Emden conjecture in four space dimensions, Adv. Math., 221, 1409, 10.1016/j.aim.2009.02.014

Zou, 2002, A priori estimates for a semilinear elliptic system without variational structure and their applications, Math. Ann., 323, 713, 10.1007/s002080200324