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- 2017
具有强奇性的半线性椭圆方程
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Abstract:
摘要 证明-div（M（x）▽u）=（f（x））/（up）正H01-解的存在性，其中M（x）是有界椭圆矩阵（即存在0< α ≤ β满足M（x）ξ·ξ ≥ α|ξ|2，|M（x）|≤ β，？x ∈ Ω，？ξ ∈ Rn）和-p <-1.本工作的关键点在于建立2个密切联系的集合，便于找到相应的能量泛函最小值。
| [1] | Liu X, Sun Y J. Multiple positive solutions for Kirchho type problems with singularity[J].Comm Pure Appl Anal, 2013, 12(2):721-733. |
| [2] | Ekeland I. On the variational principle[J].Math Anal Appl, 1974, 47:324-353. |
| [3] | Stuart C A. Existence and approximation of solutions of non-linear elliptic equations[J].Mathematische Zeitschrift, 1976, 147(1):53-63. |
| [4] | Boccardo L, Casado-Dìaz J. Some properties of solutions of some semilinear elliptic singular problems and applications to the Gconvergence[J]. Asymptotic Analysis, 2014, 86(1):1-15. |
| [5] | Arcoya D, Carmona J, Leonori T, et al. Existence and nonexistence of solutions for singular quadratic quasilinear equations[J]. Dierential Equations, 2009, 246(10):4006-4042. |
| [6] | Boccardo L. Dirichlet problems with singular and gradient quadratic lower order terms[J].ESAIM:Control, Optimisation and Calculus of Variations, 2008, 14(3):411-426. |
| [7] | Giachetti D, Murat F. An elliptic problem with a lower order term having singular behaviour[J]. Bollettino Dell Unione Matematica Italiana, 2009, 2(2):349-370. |
| [8] | Crandall M G, Rabinowitz P H, Tartar L. On a Dirichlet problem with a singular nonlinearity[J]. Communications in Partial Dierential Equations, 1977, 2(2):193-222. |
| [9] | Boccardo L, Orsina L. Semilinear elliptic equations with singular nonlinearities[J]. Calculus of Variations and Partial Dierential Equations, 2010, 37(3):363-380. |
| [10] | Boccardo L. A Dirichlet problem with singular and supercritical nonlinearities[J]. Nonli near Analysis:Theory,Methods & Applications, 2012, 75(12):4436-4440. |
| [11] | Sun Y J. Compatible phenomena in singular problems[J]. Proc Roy Soc Edinburgh, 2013,143(A):1321-1330. |
| [12] | Sun Y J, Zhang D Z. The role of the power 3 for elliptic equations with negative exponents[J]. Calculus of Variations and Partial Dierential Equations, 2014, 49(3/4):909-922. |
| [13] | Sun Y J, Wu S P. An exact estimate result for a class of singular equations with critical exponents[J]. Journal of Functional Analysis,2011, 260(5):1257-1284. |
