主要研究一类奇异拟线性椭圆型方程非平凡解的不存在性.利用变分法,通过建立一个Pohozaev型的变分恒等式,并对权函数以及参数适当假设,得到这类问题只有零解的充分条件.
[1] Assuncao RB, Carriao PC, Miyagaki OH. Subcritical perturbations of a singular quasilinear elliptic equation involving the critical Hardy-Sobolev exponent [J]. Nonlinear Analysis: An International Multidisciplinary Journal 2007, 6(6).
[2] BROCK F, ITURRIAGA L, S(A)NCHEZ J. Existence of positive solutions for p-Laplacian problems with weights [J]. Commun on Pure and Appl Anal 2006, 5(04).
[3] GHERGU M, R(A)DULESCU V. Singular elliptic problems with lack of compactness [J]. Annali di Matematica 2006, 185.
[4] Xuan B. The solvability of quasilinear Brezis-Nirenberg-type problems with singular weights [J]. Nonlinear Analysis: An International Multidisciplinary Journal 2005, 4(4).
[5] XUAN Benjin, WANG Ji. Existence of a nontrival weak solution to quasilinear elliptic equations with singular weights and multiple critical exponents [J]. Nonlinear Anal 2010, 72.
[6] Su, J., Wang, Z.-Q.. Sobolev type embedding and quasilinear elliptic equations with radial potentials [J]. Journal of Differential Equations 2011, 1(1).
[7] BERESTYCKI, LIONS H P L. Nonlinear scalar field equations, I.Existence of a ground state [J]. Archive for Rational Mechanics and Analysis 1983, 82.
[8] DING Weiyue, NI Weiming. On the existence of positive entire solutions of a semilinear elliptic equa-tion [J]. Archive for Rational Mechanics and Analysis 1986, 91.
[9] FURUSHO Y, TAKASI K, OGATA A. Symmetric positive solutions of second-order quasilinear degenerate elliptic equations [J]. Archive for Rational Mechanics and Analysis 1994, 127.
[10] NOUSSAIR E S, SWANSON C A, YANG Jianfu. Quasilinear elliptic problem with critical exponents [J]. Nonlinear Anal 1993, 20.
[11] Rodrigues, R.D.S.. On elliptic problems involving critical Hardy - Sobolev exponents and sign-changing function [J]. Nonlinear Analysis: An International Multidisciplinary Journal 2010, 4(4).
[12] Teramoto T.. On positive radial entire solutions of second-order quasilinear elliptic systems [J]. Journal of Mathematical Analysis and Applications 2003, 2(2).
[13] YU Laosen. Nonlinear p-Laplacian problems on unbounded domains [J]. Proceedings of the American Mathematical Society 1992, 115(04).
[14] DAUTRAY R, LIONS J L. Mathematical analysis and numerical methods for science and technology [M]. Berlin:Springer-Verlag 1990.
[15] KUZIN I, POHOZAEV S. Entire solutions of semilinear elliptic equations [M]. Berlin:Birkh(A)auser 1997.
