On nonlocal calculation for inhomogeneous indefinite Neumann boundary value problems

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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 \(\lambda \in (\lambda_j, \lambda_{j + 1})\).

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© Springer-Verlag Berlin/Heidelberg 2005

Authors and Affiliations

  1. 1.Mathematical DepartmentBashkir State UniversityUfaRussia

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