On singular solutions for a semilinear elliptic equation
نویسندگان
چکیده
منابع مشابه
Singular Solutions for some Semilinear Elliptic Equations
We are concerned with the behavior of u near x = O. There are two distinct cases: 1) When p >= N / ( N -2) and (N ~ 3) it has been shown by BR~ZIS & V~RON [9] that u must be smooth at 0 (See also BARAS & PIERRE [1] for a different proof). In other words, isolated singularities are removable. 2) When 1-< p < N / ( N 2) there are solutions of (1) with a singularity at x ---0. Moreover all singula...
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In this paper, we study the following elliptic problem ∆u+K(x)u p = 0 in R u > 0 in R (∗) where K(x) is a given function in Cα(R \ 0) for some fixed α ∈ (0, 1), p > 1 is a constant. Some existence, monotonicity and asymptotic expansion at infinity of solutions of (∗) are discussed. ∗Research supported in part by the Natural Science Foundation of China and NSFC †Research supported in part b...
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where K(x)μC2,b(V9 ), a, pμ(0, 1) and l is a real parameter. Such singular elliptic problems arise in the contexts of chemical heterogeneous catalysts, nonNewtonian fluids and also the theory of heat conduction in electrically conducting materials, see [3, 5, 8, 9] for a detailed discussion. Obviously (1.1) cannot have a solution uμC2(V9 ) if K(x) is not vanishing near ∂V. However, under variou...
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ژورنال
عنوان ژورنال: Kodai Mathematical Journal
سال: 1995
ISSN: 0386-5991
DOI: 10.2996/kmj/1138043352