BOUNDARY VALUE PROBLEM INVOLVING THE p-LAPLACIAN ON THE SIERPINSKI GASKET

被引：7

作者：

Priyadarshi, Amit ^{[1
]}

Sahu, Abhilash ^{[1
]}

机构：

[1] Indian Inst Technol Delhi, Dept Math, Hauz Khas, New Delhi 110016, India

来源：

FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY | 2018年 / 26卷 / 01期

关键词：

Sierpinski Gasket; p-Laplacian; Weak Solution; p-Energy; Euler Functional; NONLINEAR ELLIPTIC-EQUATIONS; FRACTAL SETS;

D O I：

10.1142/S0218348X1850007X

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study the following boundary value problem involving the weak p-Laplacian: -Delta(p)u = lambda a(x)|u|(q-1)u + b(x)|u|(l-1)u in S\S-0; u = 0 on S-0, where S is the Sierpinski gasket in R-2, S-0 is its boundary, lambda > 0, p > 1, 0 < q < p - 1 < l and a, b : S -> R are bounded nonnegative functions. We will show the existence of at least two nontrivial weak solutions to the above problem for a certain range of lambda using the analysis of fibering maps on suitable subsets.

引用

页数：13

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