Qualitative analysis of gradient-type systems with oscillatory nonlinearities on the Sierpinski Gasket

被引：17

作者：

Bonanno, Gabriele ^{[1
]}

Bisci, Giovanni Molica ^{[2
]}

Radulescu, Vicentiu ^{[3
,4
]}

机构：

[1] Univ Messina, Dept Sci Engn & Architecture, Math Sect, Fac Engn, I-98166 Messina, Italy

[2] Univ Mediterranea Reggio Calabria, Dept Patrimonio Architetton & Urbanist PAU, I-89124 Reggio Di Calabria, Italy

[3] Romanian Acad, Inst Math Simion Stoilow, Bucharest 014700, Romania

[4] Univ Craiova, Dept Math, Craiova 200585, Romania

来源：

CHINESE ANNALS OF MATHEMATICS SERIES B | 2013年 / 34卷 / 03期

关键词：

Sierpinski gasket; Nonlinear elliptic equation; Dirichlet form; Weak Laplacian; ELLIPTIC-EQUATIONS; DIFFERENTIAL-EQUATIONS; MULTIPLE SOLUTIONS; POSITIVE SOLUTIONS; DIRICHLET PROBLEM; LAPLACIAN; EXISTENCE; SPECTRUM;

D O I：

10.1007/s11401-013-0772-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Under an appropriate oscillating behavior either at zero or at infinity of the nonlinear data, the existence of a sequence of weak solutions for parametric quasilinear systems of the gradient-type on the SierpiA"ski gasket is proved. Moreover, by adopting the same hypotheses on the potential and in presence of suitable small perturbations, the same conclusion is achieved. The approach is based on variational methods and on certain analytic and geometrical properties of the SierpiA"ski fractal as, for instance, a compact embedding result due to Fukushima and Shima.

引用

页码：381 / 398

页数：18

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