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- W2077962811 abstract "with homogeneous Dirichlet conditions w,=O on dD. The function $(s) satisfies the conditions rl/ E C’[O, oo), $(Q) =O, and $‘(s)>O for s>O. Problems of this nature are of interest in reaction-diffusion processes in biology and chemistry. For example, the case for $(u) = urn, m > 1, or m E (0, 1) .for single parabolic equations (i.e., U, = du” +f(x, u)) has been studied recently for porous medium analysis and population dynamics (cf. [2, 7, 15, 18, 191). As t -+ cc these solutions tend to a solution of the corresponding elliptic scalar equation. Studies have also been carried out in these and other papers (e.g., [3, 4, 16, 171) with urn replaced by $(u) satisfying the conditions described above. In this article, however, the hypotheses on f are quite different from those in the papers mentioned above. For example, f is not necessarily Lipschitz in u and may depend discontinuously on x. Thus even for the scalar case, the results here are not covered by the other papers, although there are some overlaps. Moreover, our emphasis here is on degenerate systems (Section 3) and their applications (Section 4). These results are quite different and generalize the papers mentioned above to practical interesting cases. Other relevant results for the nondegenerate cases can be found in [S, 9, 111. In Section 2, we discuss some existence and uniqueness theorems for" @default.
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- W2077962811 date "1990-09-01" @default.
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- W2077962811 title "Existence of positive solutions for elliptic systems—Degenerate and nondegenerate ecological models" @default.
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- W2077962811 doi "https://doi.org/10.1016/0022-247x(90)90163-a" @default.
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