Results 241 to 248 of about 12,947 (248)

Periodic-parabolic eigenvalue problems with indefinite weight functions

Archiv der Mathematik, 1997
The author proves an existence and uniqueness result for the positive principal eigenvalue of a periodic-parabolic equation with \(L_\infty\) coefficients and indefinite weight. He also establishes a result on the stability of the principal positive eigenvalue with respect to the perturbations.
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Generalized principal eigenvalues for indefinite-weight elliptic problems

Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, 1998
Summary: We prove a necessary and a sufficient condition for the existence of a positive solution of the equation \((P-\mu W)u=0\) in \(\Omega\), where \(P\) is a critical, second-order, linear elliptic operator which is defined on a subdomain \(\Omega\) of a noncompact Riemannian manifold \(X\). It is assumed that \(W\in C^\alpha(\Omega)\) is a ``weak'
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ANTI-MAXIMUM PRINCIPLES FOR INDEFINITE-WEIGHT ELLIPTIC PROBLEMS

Communications in Partial Differential Equations, 2001
This paper is concerned with anti-maximum principles (AMPs) for indefinite-weight elliptic problems.
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An elliptic boundary problem involving an indefinite weight

Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2000
The spectral theory for non-self-adjoint elliptic boundary problems involving an indefinite weight function has only been established for the case of higher-order operators under the assumption that the reciprocal of the weight function is essentially bounded.
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A linear eigenvalue problem with indefinite weight function

Archiv der Mathematik, 1993
The author considers the linear eigenvalue problem \[ -\Delta u(x) = \lambda g(x) u(x) \text{ in } \mathbb{R}^ N,\;u(x) \to 0 \text{ as } | x | \to \infty, \tag{1} \] where \(N \geq 3\), \(\Delta\) denotes the Laplacian and \(g\) is a real-valued function which changes sign.
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On Principal Eigenvalues for Indefinite-Weight Elliptic Problems

1998
Consider the quantum mechanical system H μ=−Δ−μV in ℝd where μ ∈ ℝ is a spectral parameter and V ∈ C 0 ∞ (ℝd). It is well known that for d ≥ 3, the Schrodinger operator Hμ has no bound states provided that |μ| is sufficiently small. On the other hand, for d = 1, 2, B.
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Elliptic eigenvalue problems with an indefinite weight function

2001
The author considers selfadjoint elliptic eigenvalue problems of the form \(Lu= \lambda g(x)u\), \(B_j u=0 \;(j=\overline{1,m})\) on \(\Gamma \), where \(L\) is an elliptic operator of order \(2m\) defined on a bounded open set \( G \subset\mathbb R^n\) (\(n \geq 1\)) with boundary \(\Gamma \), the \(B_j\)'s are linear differential operators defined on
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Elliptic Boundary Value Problems with Indefinite Weights +

1997
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