Exact Multiplicity of Sign-Changing Solutions for a Class of Second-Order Dirichlet Boundary Value Problem with Weight Function

Using bifurcation techniques and Sturm comparison theorem, we establish exact multiplicity results of sign-changing or constant sign solutions for the boundary value problems u″+a(t)f(u)=0, t∈(0, 1), u(0)=0, and u(1)=0, where f∈C(ℝ,ℝ) satisfies f(0)=0 and the limits f∞=lim|s|→∞(f(s)/s), f0=lim|s|→0(f(s)/s)∈{0,∞}. Weight function a(t)∈C1[0,1] satisfies a(t)>0 on [0,1]