D. V. Tunitsky, “On solvability of semilinear second-order elliptic equations on closed manifolds”, Izv. RAN. Ser. Mat., 2022, Volume 86, Issue 5,Pages <nobr>97

This article is cited in 8 papers

On solvability of semilinear second-order elliptic equations on closed manifolds

D. V. Tunitsky^ab

^a V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, Moscow
^b Lomonosov Moscow State University

Abstract: The paper is concerned with solvability in the class of weak solutions of one class of semilinear elliptic second-order differential equations on arbitrary closed manifolds. These equations are inhomogeneous analogues of the stationary Kolmogorov–Petrovskii–Piskunov–Fisher equation, and have great applied and mathematical value.

Keywords: Kolmogorov–Petrovskii–Piskunov–Fisher equation, stationary solutions, nonlinear elliptic equations on manifolds, weak solutions, strong solutions.

UDC: 517.956.25+517.956.22+517.954

MSC: Primary 35L70; Secondary 35L60, 58A17

Received: 01.09.2021

DOI: 10.4213/im9261