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Funktsional. Anal. i Prilozhen., 2007, Volume 41, Issue 1, Pages 23–38 (Mi faa1761)  

This article is cited in 12 scientific papers (total in 12 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


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English version:
Functional Analysis and Its Applications, 2007, 41:1, 18–30

Bibliographic databases:

UDC: 517.957+517.972.5
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

Citation in format AMSBIB
\by Ya.~Sh.~Il'yasov
\paper Bifurcation Calculus by the Extended Functional Method
\jour Funktsional. Anal. i Prilozhen.
\yr 2007
\vol 41
\issue 1
\pages 23--38
\jour Funct. Anal. Appl.
\yr 2007
\vol 41
\issue 1
\pages 18--30

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    This publication is cited in the following articles:
    1. Il'yasov Ya., “A duality principle corresponding to the parabolic equations”, Phys. D, 237:5 (2008), 692–698  crossref  mathscinet  zmath  isi
    2. Lubyshev V., “Precise range of the existence of positive solutions of a nonlinear, indefinite in sign Neumann problem”, Commun. Pure Appl. Anal., 8:3 (2009), 999–1018  crossref  mathscinet  zmath  isi  elib
    3. Il'yasov Ya., Runst Th., “Positive solutions of indefinite equations with p-Laplacian and supercritical nonlinearity”, Complex Var. Elliptic Equ., 56:10-11 (2011), 945–954  crossref  mathscinet  zmath  isi
    4. A. A. Ivanov, Ya. Sh. Ilyasov, “Nakhozhdenie bifurkatsii dlya reshenii nelineinykh uravnenii metodami kvadratichnogo programmirovaniya”, Zh. vychisl. matem. i matem. fiz., 53:3 (2013), 350–364  mathnet  crossref  zmath  elib
    5. Bobkov V., Il'Yasov Ya., “Asymptotic Behaviour of Branches for Ground States of Elliptic Systems”, Electron. J. Differ. Equ., 2013, 212  mathscinet  zmath  isi  elib
    6. Bobkov V., Tanaka M., “on Positive Solutions For (P, Q)-Laplace Equations With Two Parameters”, Calc. Var. Partial Differ. Equ., 54:3 (2015), 3277–3301  crossref  mathscinet  zmath  isi  elib
    7. Il'yasov Ya., Ivanov A., “Computation of Maximal Turning Points To Nonlinear Equations By Nonsmooth Optimization”, Optim. Method Softw., 31:1 (2016), 1–23  crossref  mathscinet  zmath  isi
    8. Bobkov V., Il'yasov Ya., “Maximal existence domains of positive solutions for two-parametric systems of elliptic equations”, Complex Var. Elliptic Equ., 61:5 (2016), 587–607  crossref  mathscinet  zmath  isi  elib  scopus
    9. Ilyasov Ya.Sh., “Bifurcation and Blow-Up Results For Equations With P-Laplacian and Convex-Concave Nonlinearity”, Electron. J. Qual. Theory Differ., 2017, no. 96, 1–13  crossref  mathscinet  isi
    10. Bobkov V., Tanaka M., “Remarks on Minimizers For (P, Q)-Laplace Equations With Two Parameters”, Commun. Pure Appl. Anal, 17:3 (2018), 1219–1253  crossref  mathscinet  zmath  isi  scopus
    11. Bobkov V., Tanaka M., “On the Fredholm-Type Theorems and Sign Properties of Solutions For (P, Q)-Laplace Equations With Two Parameters”, Ann. Mat. Pura Appl., 198:5 (2019), 1651–1673  crossref  mathscinet  zmath  isi
    12. Paz Salazar P.D., Ilyasov Ya., Costa Alberto L.F., Marques Costa E.C., Salles M.B.C., “Saddle-Node Bifurcations of Power Systems in the Context of Variational Theory and Nonsmooth Optimization”, IEEE Access, 8 (2020), 110986–110993  crossref  isi
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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