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- W2049647869 abstract "Abstract We are concerned with existence results for nonlinear scalar Neumann boundary value problems u ″ + g ( x, u ) = 0, u ′(0) = u ′(π) = 0 where g ( x, u ) satisfies Carathéodory conditions and is (possibly) unbounded. On the one hand we only assume that the function (sgn u ) g ( x, u ) is bounded either from above or from below in some function space, and we impose conditions which relate the asymptotic behavior of the function (for¦ u ¦large) with the first two eigenvalues of the corresponding linear problem (here G ( x, u ) = is the potential generated by g ). On the other hand we consider cases where the function (sgn u ) g ( x, u ) is unbounded. The potential G(x, u) is not necessarily required to satisfy a convexity condition. Our method of proof is variational, we make use of the Saddle Point Theorem." @default.
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- W2049647869 date "1993-12-01" @default.
- W2049647869 modified "2023-09-24" @default.
- W2049647869 title "Saddle point theorem and nonlinear scalar Neumann boundary value problems" @default.
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- W2049647869 doi "https://doi.org/10.1017/s144678870003411x" @default.
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