科研之友
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摘要
This paper is concerned with the existence of multiple non-radial positive solutions for @@@ {-Delta u + (1 + beta V(y))u = vertical bar u vertical bar(p-2)u y is an element of R-N @@@ u(y) -> 0 as vertical bar y vertical bar -> + infinity @@@ where 2 < p < 2*, 2* = 2N/N-2 for N > 2 and 2* = +infinity for N = 2, beta can be regarded as a parameter and V(vertical bar y vertical bar) > 0 decays exponentially to zero at infinity. We prove that, for any positive integer k > 1, there exists a suitable range of beta such that the above problem has a non-radial positive solution with exactly k maximum points which tending to infinity as beta -> +infinity(or 0(+)).
