Abstract
This paper investigates properties of certain nonlinear PDEs on fractal sets. With an appropriately defined Laplacian, we obtain a number of results on the existence of non-trivial solutions of the semilinear elliptic equation Delta u + a(x)u = f(x, u), with zero Dirichlet boundary conditions, where u is defined on the Sierpinski gasket. We use the mountain pass theorem and the saddle point theorem to study such equations for different classes of a and f. A strong Sobolev-type inequality leads to properties that contrast with those for classical domains. (C) 1999 Academic Press.
Original language | English |
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Pages (from-to) | 552-573 |
Number of pages | 22 |
Journal | Journal of Mathematical Analysis and Applications |
Volume | 240 |
Publication status | Published - 15 Dec 1999 |
Keywords
- Sierpinski gasket
- Laplacian operator
- weak solution
- mountain pass theorem
- saddle point theorem
- Sobolev-type inequality
- FRACTALS