Abstract:

This paper considers the existence and multiplicity of positive solutions for second-order periodic boundary value problems $\left\{\begin{array}{l}u^{\prime \prime}(t)+p u^{\prime}(t)+q u(t)=\lambda f(t, u(t)), t \in(0, 2 \pi), \\u(0)=u(2 \pi), u^{\prime}(0)=u^{\prime}(2 \pi), \end{array}\right.$ where p, q>0 are constants and satisfy p²>4q, λ>0 is a parameter, f: [0, 2π]×[0, +∞)→[0, +∞) is continuous. The proof of the main results are based on the fixed point theorem of cone expansion-compression.

Key words: second-order, periodic boundary value problems, fixed point theorem, multiplicity