Existence of critical elliptic systems with boundary singularities

• Autorzy: Yang J. , Zhou Y.
• Języki publikacji: EN

Abstrakty

EN

In this paper, we are concerned with the existence of positive solutions of the following nonlinear elliptic system involving critical Hardy-Sobolev exponent [formula] where N ≥4 and Ω is a C1 bounded domain in RN with [formula].The case when 0 belongs to the boundary of Ω is closely related to the mean curvature at the origin on the boundary. We show in this paper that problem (*) possesses at least a positive solution.

Słowa kluczowe

EN

existence; compactness; critical Hardy-Sobolev exponent; nonlinear system

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2013
• Tom: Vol. 33, no. 2
• Strony: 373--390
• Opis fizyczny: Bibliogr. 14 poz.

Twórcy

autor

Yang J.

• Jiangxi Normal University Department of Mathematics Nanchang, Jiangxi 330022, P.R. China

autor

Zhou Y.

• Jiangxi Normal University Department of Mathematics Nanchang, Jiangxi 330022, P.R. China

Bibliografia

• [1] CO. Alves, D.C. de Morais Filho, M.A.S. Souto, On systems of elliptic equations involving subcritical and critical Sobolev exponents, Nonlinear Anal. 42 (2000), 771-787.
• [2] H. Brezis, L. Nirenberg, Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents, Comm. Pure Appl. Math. 36 (1983), 437-477.
• [3] L. Caffarelli, R. Kohn, L. Nirenberg, First order interpolation inequality with weights, Compos. Math. 53 (1984), 259-275.
• [4] H. Egnell, Positive solutions of semilinear equations in cones, Trans. Amer. Math. Soc. 11 (1992), 191-201.
• [5] N. Ghoussoub, X.S. Kang, Hardy-Sobolev critical elliptic equations with boundary Parities, Ann. Inst. H. Poincare Anal. Non Lineaire 21 (2004), 769-793.
• [6] N. Ghoussoub, F. Robert, The effect of curvature on the best constant in the Hardy-Sobolev inequalities, Geom. Funct. Anal. 16 (2006), 1201-1245.
• [7] N. Ghoussoub, F. Robert, Concentration estimates for Emden-Fowler equations with boundary singularities and critical growth, IMRP Int. Math. Res. Pap. 21867 (2006), 1-85.
• [8] N. Ghoussoub, F. Robert, Elliptic equations with critical growth and a large set of boundary singularities, Trans. Amer. Math. Soc. 361 (2009), 4843-4870.
• [9] C.H. Hsia, C.S. Lin, H. Wadade, Revisiting an idea of Brezis and Nirenberg, J. Funct. Anal. 259 (2010), 1816-1849.
• [10] Haiyang He, Jianfu Yang, Positive solutions for critical elliptic systems in non-contractible domain, Nonlinear Anal. 70 (2009), 952-973.
• [11] P.L. Lions, The concentration-compactness principle in the calculus of variations. The locally compact case, Ann. Inst. H. Poincare Anal. Non Lineaire 1 (1984), 109-145 and 223-283.
• [12] C.S. Lin, H. Wadade, Minimizing problems for the Hardy-Sobolev type inequality with the sigularity on the boundary, preprint 2011.
• [13] G. Talenti, Best constant in Sobolev inequality, Ann. Mat. Pura Appl. 110 (1976), 353-372.
• [14] Zhongwei Tang, Sign-changing solutions of critical growth nonlinear elliptic systems, Nonlinear Anal. 64 (2006), 2480-2491.