The Dirichlet problem for second order semilinear elliptic and parabolic equations
نویسندگان
چکیده
منابع مشابه
The Dirichlet Problem for Second Order Semilinear Elliptic and Parabolic Equations
In the present paper the Dirichlet problem for semilinear elliptic and parabolic equations in general form is considered. New condition guaranteeing the global solvability of this problem for a wide class of superlinear sources, including e u and |u|p−1u , p > 1 , is formulated. For sublinear case (for example ln(1+ |u|) or |u|p−1u , p < 1) this condition is automatically fulfilled. Our approac...
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and repeated indices indicate summation from 1 to n. The functions a'(x, u, p), a(x, u, p) are defined in QX£ n + 1 . If furthermore for any ikf>0, the ratio of the maximum to minimum eigenvalues of [a(Xy u, p)] is bounded in ÛX( — M, M)XE, Qu is called uniformly elliptic. A solution of the Dirichlet problem Qu = Q, u—<f)(x) on <50 is a C(n)P\C(O) function u(x) satisfying Qu = 0 in £2 and agree...
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ژورنال
عنوان ژورنال: Differential Equations & Applications
سال: 2009
ISSN: 1847-120X
DOI: 10.7153/dea-01-22