Multiplicity Solutions to a Doubly Eigenvalue Fourth-Order Equation

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Authors

  • Department of Science, Sichuan University of Science and Engineering, Zigong 643000 ,CN
  • Department of Mathematics, Faculty of Sciences, Razi University, Kermanshah 67149 ,IR

Keywords:

Three Solutions, Critical Point, Multiplicity Results, Navier Problem.

Abstract

In this paper, using a three critical points theorem and variational methods, we study the existence of at least three solutions for the following fourth-order boundary value problem on a compact interval [a, b] ⊆ R {uiv + αu"+βu = λf(x, u) + μg(x, u) x ∈ (a,b), u(a) = u(b) = u"(a) = u"(b) = 0) where α, β are real constants and λ, μ are positive parameters and f, g: (a,b) í— R → R are L2-Caratheodory functions.