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Boundary value problems with indefinite weights and applications Fethi Bin Muhammad Belgacem Department of Mathematics and Computer Science College of Science, Kuwait University P.O.Box 5969 Safat 13060 Kuwait e-mail: belgacem@math-1.kuniv.edu.kw A uniformly elliptic model L : L[u]= Ñ × [-aÑ u + bu] = l mu, describing the stationary dynamics of a population with density u=u(x) subject to a diffusion matrix a = (aij (x)), a drift vector b = (bi (x)) and a sign indefinite growth rate m = m(x) in a bounded region W Ì Â n, is treated. A minimax characterization of the Dirichlet principal eigenvalue (l D*). Theorem: For a properly defined spaces F 1 and proper conditions on the coefficients b, a and m, (l D*) may be characterized as follow:  These formulations coincide with those of Manes-Micheletti when the operator is self-adjoint, those of Donsker-Varadhan when m=1, and those of Holland when the weight m is positive. |
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