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On positive solutions of nonlinear elliptic eigenvalue problems

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Summary

Suppose Ω is a bounded region inR n. In this paper we investigate the equationLu=λF(x, u),u|∂Ω=0 whereL is an elliptic partial differential operator and V 3F(x, t) is a positive function on ΩxR 1 which may have jump discontinuities with respect tot. We show that if certain conditions are satisfied there exists an unbounded continuum Λ of solutions (γ, u), withu(x)≥0, in the spaceR 1×S. HereS is a Banach space of real valued functions such as\(C\left( {\bar \Omega } \right) \)

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  1. Tempe, U.S.A.

    Hendrik J. Kuiper

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  1. Hendrik J. Kuiper
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Introduced by G. Fichera.

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Kuiper, H.J. On positive solutions of nonlinear elliptic eigenvalue problems. Rend. Circ. Mat. Palermo 20, 113–138 (1971). https://doi.org/10.1007/BF02844166

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