摘要 : In this paper we study positive solutions for the Kirchhoff type equation -M (x, vertical bar vertical bar u vertical bar vertical bar(2) ) Delta u =lambda f(u) with Dirichlet boundary conditions in a bounded domain Omega, where v... 展开 In this paper we study positive solutions for the Kirchhoff type equation -M (x, vertical bar vertical bar u vertical bar vertical bar(2) ) Delta u =lambda f(u) with Dirichlet boundary conditions in a bounded domain Omega, where vertical bar vertical bar center dot vertical bar vertical bar is the norm in H-0(1)(Omega) and f, M are suitable functions. The problem is nonvariational since the nonlocal coefficient M, possibly degenerate, depends on the point x is an element of Omega. We show that these properties of M can produce interesting phenomena, even with simple homogeneous right hand sides, providing existence, nonexistence, and multiplicity results, due to the fact that the rate of growth with respect to u on the left hand side may change in Omega. Several model examples are given, including one where M takes the form of the original Kirchhoff coefficient for the elastic string, but with nonhomogeneous material. 收起