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Sufficient Conditions of Uniqueness for The Regular Solution of a Special Class of Nonlinear Boundary Value Problems

Part of the International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale D’Analyse Numérique book series (ISNM, volume 19)

Abstract

Let Ω ⊂ R m be a bounded, closed domain and let Γ be its boundary. For the simplicity let us consider that this boundary is a smooth, closed curve. Le A be an elliptic operator
$$Au = \sum\limits_{{i,j = 1}}^{m} {{H_{{ij}}}(x)\frac{{{\partial ^{2}}u}}{{\partial {x_{i}}\partial {x_{j}}}} + \sum\limits_{{i = 1}}^{m} {{K_{i}}(x)\frac{{\partial u}}{{\partial {x_{i}}}} + C(x)u} } $$
(1)
Such that the problem
$$\begin{gathered} Au + \lambda u = 0 \hfill \\ u{|_{\Gamma }} = 0 \hfill \\ \end{gathered} $$
(2)
allows an infinite sequence of regular eigenfunction {u i }iN and eigenvalues {λ i }iN.

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Copyright information

© Springer Basel AG 1974

Authors and Affiliations

  • I. Toma
    • 1
  1. 1.BukarestRumänien

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