Existence of Positive Entire Solutions of Semilinear Elliptic Equations on Rn
نویسنده
چکیده
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 type. To overcome this kind of difficulty, P. L. Lions developed the concentrate compactness method [8, 9], and established the following result: Assume that lim|x|→∞Q(x) = Q(> 0) and Q(x) ≥ Q on R . Then the problem (PQ) has a positive solution. This result is based on the observation that the ground state level cQ of the functional
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