Separation structure of positive radial solutions of a semilinear elliptic equation in Rn
نویسندگان
چکیده
منابع مشابه
Separation property of solutions for a semilinear elliptic equation
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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has been studied by several authors, where 1 < p for N = 2, 1 < p < (N + 2)/(N − 2) for N ≥ 3 and Q(x) is a positive bounded continuous function. If Q(x) is a radial function, we can find infinity many solutions of problem (PQ) by restricting our attention to the radial functions (cf. [2, 5]). IfQ(x) is nonradial, we encounter a difficulty caused by the lack of a compact embedding of Sobolev ty...
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(see for example [3], [8], [9], [14], [17]–[19], [24] and the references therein). Here, λ ∈ R is a positive parameter, k is a given smooth function on R, n ≥ 3, and 2∗ = 2n/(n− 2) is the critical Sobolev exponent. Problem (0) has a geometrical relevance, since for λ = 0 every solution to (0) gives rise, up to a stereographic projection, to a metric g on the sphere whose scalar curvature is pro...
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ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 2003
ISSN: 0022-0396
DOI: 10.1016/s0022-0396(03)00172-4