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This article is cited in 16 scientific papers (total in 16 papers)
Bifurcation Calculus by the Extended Functional Method
Ya. Sh. Il'yasov Bashkir State University
Abstract:
We justify variational principles of a new type corresponding to bifurcations of solutions for families of equations given in variational form. To illustrate the method, we consider elliptic equations with sign-indefinite nonlinearities and prove the existence of pairwise creation-annihilation bifurcations of their positive solutions. The corresponding bifurcation points are expressed via explicitly specified variational principles.
Keywords:
bifurcation of solutions, minimax problem, elliptic equation, sign-indefinite nonlinearity.
Received: 10.06.2005
Citation:
Ya. Sh. Il'yasov, “Bifurcation Calculus by the Extended Functional Method”, Funktsional. Anal. i Prilozhen., 41:1 (2007), 23–38; Funct. Anal. Appl., 41:1 (2007), 18–30
Linking options:
https://www.mathnet.ru/eng/faa1761https://doi.org/10.4213/faa1761 https://www.mathnet.ru/eng/faa/v41/i1/p23
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Abstract page: | 634 | Full-text PDF : | 285 | References: | 69 | First page: | 3 |
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