A unified treatment using critical point methods of the existence of multiple solutions for superlinear and sublinear neumann problems
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2011-05-01Author
Motreanu, D.
O'Regan, Donal
Papageorgiou, Nikolaos S.
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Motreanu, D. O'Regan, Donal; Papageorgiou, Nikolaos S. (2011). A unified treatment using critical point methods of the existence of multiple solutions for superlinear and sublinear neumann problems. Communications on Pure and Applied Analysis 10 (6), 1791-1816
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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.