科研之友
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摘要
We are concerned with the existence of single- and multi-bump solutions of the equation -Delta u + (lambda a (x) + a(0)(x))u = vertical bar u vertical bar(p-2) u, x is an element of R-N; here p > 2, and p < 2N/N-2 if N >= 3. We require that a >= 0 is in L-loc(infinity) (R-N) and has a bounded potential well Omega, i.e. a(x) = 0 for x is an element of Omega and a (x) > 0 for x is an element of R-N\(Omega) over bar. Unlike most other papers on this problem we allow that a(0) is an element of L-infinity (R-N) changes sign. Using variational methods we prove the existence of multibump solutions u lambda which localize, as lambda -> infinity, near prescribed isolated open subsets Omega(1); . . . , Omega(k) subset of Omega. The operator L-0 :=- -Delta+ a(0) may have negative eigenvalues in Omega(j), each bump of u lambda may be sign-changing.
- 出版日期2013-1
- 单位北京师范大学
