Abstract
Abstract We shall study the existence and multiplicity of nodal solutions of the nonlinear second-order two-point boundary value problems, u ″ + f ( t , u ) = 0 , t ∈ ( 0 , 1 ) , u ( 0 ) = u ( 1 ) = 0 . The proof of our main results is based upon bifurcation techniques. Mathematics Subject Classifications: 34B07; 34C10; 34C23.
Highlights
1 Introduction In [1], Ma and Thompson were considered with determining interval of μ, in which there exist nodal solutions for the boundary value problem (BVP)
[0, 1], and the inequality is strict on some subset of positive measure in (0,1), where lk denotes the kth eigenvalue of u (t) + λu(t) = 0, t ∈ (0, 1), u(0) = u(1) = 0; (1:5)
2 Preliminary results To show the nodal solutions of the BVP (1.4), we need only consider an operator equation of the following form u = λAu
Summary
Let μk be the kth eigenvalue of (1.2) and k be an eigenfunction corresponding to μk, k has exactly k – 1 simple zeros in (0,1) (see, e.g., [2]).
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