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On nonlocal calculation for inhomogeneous indefinite Neumann boundary value problems

Authors:	Yavdat Il’yasov Thomas Runst

Institution:	(1) Mathematical Department, Bashkir State University, 450074 Ufa, Russia;(2) Mathematisches Institut, Friedrich-Schiller-Universität Jena, 07740 Jena, Germany

Abstract:	This paper concerns with a family of inhomogeneous Neumann boundary value problems having indefinite nonlinearities which depend on a real parameter $\lambda$ . We discuss the existence and the multiplicity of positive solutions with respect to $\lambda$ . Developing the fibering method further, we can introduce a constructive concept of the calculation of certain nonlocal intervals $(\lambda_j, \lambda_{j + 1}) \subseteq \mathbb{R}$ , the so-called sufficient intervals of the existence. Then we are able to prove some new results on the existence and the multiplicity of positive solutions $u_{\lambda}$ for $\lambda \in (\lambda_j, \lambda_{j + 1})$ .Received: 22 December 2003, Accepted: 29 January 2004, Published online: 16 July 2004Mathematics Subject Classification (2000): 35J70, 35J65, 47H17

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