Existence of multi-bump solutions for a class of Kirchhoff type problems in R3

Using variational methods, we establish existence of multi-bump solutions for a class of Kirchhoff type problems -(a + b integral(R3)vertical bar del u vertical bar(2)dx)Delta u +lambda V(x) u = f(u), where f is a continuous function with subcritical growth, V( x) is a critical frequency in the sense that inf(x epsilon R3) V(x) = 0. We show that if the zero set of V( x) 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 there exists, for any non-empty subset J subset of {1,..., k}, a bump solution is trapped in a neighborhood of boolean OR(j epsilon J)Omega(j). (C) 2013 AIP Publishing LLC.