On Conditions of the Nonexistence of Solutions of Nonlinear Equations with Data from Classes Close to L
On Conditions of the Nonexistence of Solutions of Nonlinear Equations with Data from Classes Close to L
摘要
We establish conditions of the nonexistence of weak solutions of the Dirich- let problem for nonlinear elliptic equations of arbitrary even order with some right- hand sides from Lm where m ~ 1. The conditions include the requirement of a certain closeness of the parameter m to 1.
参考文献9
-
1B6nilan P., Boccardo L., Gallout %, Gariepy R., Pierre M. and Vazquez J. L., An Ll-theory of existence and uniqueness of solutions of nonlinear elliptic equations. Ann. Scuola Norm. Sup. Pisa CI. Sci. (4), 22 (1995), 241-273.
-
2Kovalevskii A. A., Skrypnik I. I. and Shishkov A. E., Singular Solutions of Nonlinear Elliptic and Parabolic Equations. Naukova Dumka, Kyiv, 2010. (in Russian).
-
3Kovalevsky A. A. and Nicolosi F., On a condition for the nonexistence of W-solutions of nonlinear high-order equations with Ll-data. Cubo, 14 (2012), 189-196.
-
4Kovalevskii A. A., Entropy solutions of the Dirichlet problem for a class of non-linear elliptic fourth-order equations with right-hand sides in L1. Izv. Math., 65 (2001), 231-283.
-
5Kovalevsky A. and Nicolosi F., Solvability of Dirichlet problem for a class of degenerate nonlinear high-order equations with Ll-data. Nonlinear Anal., 47 (2001), 435-446.
-
6Yosida K., Functional Analysis. Springer-Verlag, Berlin, 1965.
-
7Lions J.-L., Quelques M6thodes de R6solution des Problmes aux Limites Non Lin6aires. Dunod, Gauthier-Villars, Paris, 1969.
-
8Boccardo L. and Gallout T., Nonlinear elliptic equations with right hand side measures. Comm. Partial Differential Equations, 17 (1992), 641-655.
-
9Kovalevskii A. A., Integrability of solutions of nonlinear elliptic equations with right-hand sides from classes close to L1. Math. Notes, 70 (2001), 337-346.
-
1龙薇,杨健夫.临界增长Hénon方程解的存在性[J].江西师范大学学报（自然科学版）,2010,34(5):463-466. 被引量：2
-
2TANG Lin-shan,JIANG Cheng-shun.Existence of Solutions to the Higher Order Nonlinear Differential Equations[J].Chinese Quarterly Journal of Mathematics,2012,27(1):1-10.
-
3R.P.AGARWAL,P.S.KELEVEDJIEV.Existence of Solutions to a Singular Initial Value Problem[J].Acta Mathematica Sinica,English Series,2007,23(10):1797-1806.
-
4TAO Xiang-xing FANG Yi.The Regularity Estimates for the Elliptic Equations in Orlicz Classes[J].Chinese Quarterly Journal of Mathematics,2012,27(1):29-35.
-
5ZHANG Shao-fei,LI Hui-zhen.Two Classes of Solvable Subgroups of SL（3, C） and Application for Differential Equations in C[J].Chinese Quarterly Journal of Mathematics,2010,25(1):30-36. 被引量：1
-
6Bin ZHAO1,2 1.Department of Mathematics,Northwest Agriculture & Forestry University,Shaanxi 712100,P.R.China,2.Department of Mathematics,Northwest University,Shaanxi 710127,P.R.China.Dynamics of Two Extensive Classes of Recursive Sequences[J].Journal of Mathematical Research and Exposition,2010,30(5):929-935.
-
7吴卓人.ON SAKAGUCHI CLASSES OF SCHLICHT FUNCTIONS[J].Chinese Science Bulletin,1985,30(12).
-
8Huang Benwen.The Characterization of A_(5)[J].Wuhan University Journal of Natural Sciences,1997,2(4):23-28. 被引量：5
-
9Cai Hao-tao,Du Jin-yuan.Non-normal Hasemann Boundary Value Problem[J].Wuhan University Journal of Natural Sciences,2001,6(3):649-651.
-
10Jiaqi Mo.SINGULARLY PERTURBED SOLUTION FOR THIRD ORDER NONLINEAR EQUATIONS WITH TWO PARAMETERS[J].Analysis in Theory and Applications,2007,23(4):301-306.
