The first eigenvalue of quasilinear elliptic operators and its applications (Q2706024)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The first eigenvalue of quasilinear elliptic operators and its applications |
scientific article |
Statements
26 March 2001
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pseudo-Laplacian
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the first eigenvalue
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global bifurcations
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weak comparison principle
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maximum principles
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positive solutions
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The first eigenvalue of quasilinear elliptic operators and its applications (English)
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The author of this interesting paper presents results concerning the basic properties of the first eigenvalue of some quasilinear elliptic operators with the Dirichlet boundary condition in bounded domains. Its applications to the bifurcation theory, the equivalence of maximum principles as well as the existence and uniqueness of positive solutions are discussed. It is proved the existence of bifurcation points for a certain elliptic boundary problem. Two interesting results being obtained here are a weak comparison principle and also a maximum principle. The existence of nonnegative and positive solutions is discussed as well.
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