Positive solutions of fourth-order periodic boundary value problems☆

By Yongxiang Li. 2003

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Abstract In this paper the existence results of positive solutions are obtained for fourth-order periodic boundary value problem u (4) −βu″+αu=f(t, u), 0⩽t⩽1, u (i) (0)=u (i) (1), i=0,1,2,3, where f : [0, 1]× R + → R + is continuous, α, β∈ R and satisfy 0 −2π2,α/π4+β/π2+1>0. The discussion is based on a new maximum principle for operator L 4 u=u (4) −βu″+αu in periodic boundary condition and fixed point index theory in cones.

Subfields: Applied Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/edeccf415b0ec68e0ec8329be0c20e914afbf89a