A unified treatment using critical point
methods of the existence of multiple solutions for superlinear and
sublinear Neumann problems
D. Motreanu - Département de Mathématiques, Université de Perpignan, Avenue de Villeneuve 52, 66860 Perpignan Cedex, France (email)
Abstract: In this paper we present a framework which permits the unified treatment of the existence of multiple solutions for superlinear and sublinear Neumann problems. Using critical point theory, truncation techniques, the method of upper-lower solutions, Morse theory and the invariance properties of the negative gradient flow, we show that the problem can have seven nontrivial smooth solutions, four of which have constant sign and three are nodal.
Keywords: Superlinear and
sublinear problems, critical point theory, truncation techniques,
upper-lower solutions, Morse theory, gradient flow, multiple
Received: May 2010; Revised: March 2011; Published: May 2011.
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