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Zh. Vychisl. Mat. Mat. Fiz., 2017, Volume 57, Number 3, Pages 491–509 (Mi zvmmf10539)  

On the curve of critical exponents for nonlinear elliptic problems in the case of a zero mass

Ya. Sh. Il'yasov

Institute of Mathematics, Ufa Scientific Center, Russian Academy of Sciences, Ufa, Bashkortostan, Russia

Abstract: For semilinear elliptic equations $-\Delta u=\lambda|u|^{p-2}u-|u|^{q-2}u$, boundary value problems in bounded and unbounded domains are considered. In the plane of exponents $p\times q$, the so-called curves of critical exponents are defined that divide this plane into domains with qualitatively different properties of the boundary value problems and the corresponding parabolic equations. New solvability conditions for boundary value problems, conditions for the stability and instability of stationary solutions, and conditions for the existence of global solutions to parabolic equations are found.

Key words: critical exponent, Pohozaev' identity, fibering method, stability of solutions.

Funding Agency Grant Number
Russian Foundation for Basic Research 14-01-00736_a


DOI: https://doi.org/10.7868/S0044466917030061

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English version:
Computational Mathematics and Mathematical Physics, 2017, 57:3, 497–514

Bibliographic databases:

UDC: 519.63
Received: 26.07.2016

Citation: Ya. Sh. Il'yasov, “On the curve of critical exponents for nonlinear elliptic problems in the case of a zero mass”, Zh. Vychisl. Mat. Mat. Fiz., 57:3 (2017), 491–509; Comput. Math. Math. Phys., 57:3 (2017), 497–514

Citation in format AMSBIB
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  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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