Electron. J. Diff. Equ., Vol. 2015 (2015), No. 200, pp. 1-11.

Existence and multiplicity of solutions for semilinear elliptic equations with Neumann boundary conditions

Qin Jiang, Sheng Ma

Abstract:
This article shows the existence of solutions by the least action principle, for semilinear elliptic equations with Neumann boundary conditions, under critical growth and local coercive conditions. In the subcritical growth and local coercive case, multiplicity results are established by using the minimax methods together with a standard eigenspace decomposition.

Submitted May 29, 2015. Published August 4, 2015.
Math Subject Classifications: 35J20, 35J25.
Key Words: Elliptic equations; Neumann boundary conditions; critical point; least action principle; minimax methods.

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Qin Jiang
Department of Mathematics
Huanggang Normal University
Hubei 438000, China
email: jiangqin999@126.com
Sheng Ma
Department of Mathematics
Huanggang Normal University
Hubei 438000, China
email: masheng666@126.com

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