The Existence of Nodal Solutions for the Half-Quasilinear p-Laplacian Problems

摘要

In this paper,we study the existence of nodal solutions for the following problem:-((φ)p(x'))'=α(t)(φ)p(x+)+β(t)(φ)p(x-) + ra(t)f(x),0＜t＜1,x(0)=x(1)=0,where (φ)p(s)=|s|p-2s,a ∈ C([0,1],(0,∞)),x+=max{x,0},x-=-min{x,0},α(t),β(t) ∈C[0,1];f ∈ C(R,R),sf(s)＞0 for s≠0,and f0,f∞ (∈) (0,∞),where f0=lim|s|→0f(s)/(φ)p(x),f∞ =lim|s|→∞ f(s)/(φ)p(s).We use bifurcation techniques and the approximation of connected components to prove our main results.