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Mat. Zametki, 2011 Volume 89, Issue 2, Pages 260–271 (Mi mzm8935)
Existence of Multiple Solutions of Higher-Order Nonlinear Elliptic Equations

V. F. Lubyshev

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: We study the existence of multiple solutions for a class of even-order nonlinear elliptic equations with the Dirichlet boundary conditions. We also study the corresponding nonlinear Hamiltonian system of higher-order linear equations.

Keywords: higher-order elliptic equation, convex-concave nonlinearity, multiple solutions, fibering method, variational method, Hamiltonian system, Dirichlet problem.

UDC: 517

Received: 29.09.2010

DOI: 10.4213/mzm8935


 English version: Mathematical Notes, 2011, 89:2, 255–265

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© Steklov Math. Inst. of RAS, 2024