Nonlinear elliptical equations on the Sierpiński gasket (Q1970003)
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scientific article; zbMATH DE number 1417581
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Nonlinear elliptical equations on the Sierpiński gasket |
scientific article; zbMATH DE number 1417581 |
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Nonlinear elliptical equations on the Sierpiński gasket (English)
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25 July 2000
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The authors investigate a question on the nontrivial solutions for the equation \(\Delta u + a(x)u=f(x,u)\) with zero Dirichlet conditions on the Sierpiński gasket. There are results both for a standard (in this theory) Laplacian and for a weak one. Some of the used general functional tools are: mountain pass theorem and saddle point theorem.
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Sierpiński gasket
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Laplacian operator
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weak solution
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mountain pass theorem
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saddle point theorem
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Sobolev-type inequality
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