科研之友
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摘要
Using variational methods, we establish existence of multi bump solutions for a class of Kirchhoff type problems @@@ -(1 + b integral(RN) vertical bar del u vertical bar(p) dx) Delta(p)u + (lambda V(x) + Z(x))u(p-1) = alpha f(u) + u(p*-1), @@@ where f is a continuous function, V, Z: R-N -> R are continuous functions verifying some hypotheses. We show that if the zero set of V has several isolated connected components Omega(1),..., Omega(k) such that the interior of Omega(i) is not empty and partial derivative Omega(i) is smooth, then for lambda > 0 large enough there exists, for any non-empty subset Gamma subset of {1,..., k}, a bump solution trapped in a neighbourhood of boolean OR(j is an element of Gamma) Omega(j). The results are also new for the case p = 2.
