Boundary Value Problems for a Super-Sublinear Asymmetric Oscillator : The Exact Number of Solutions

Abstract EN

Properties of asymmetric oscillator described by the equation x′′=−λ(x+)p+μ(x−)q (i), where p≥1 and 0

A set of (λ,μ) such that the problem (i), x(0)=0=x(1) (ii), and |x′(0)|=α (iii) have a nontrivial solution, is called α-spectrum.

We give full description of α-spectra in terms of solution sets and solution surfaces.

The exact number of nontrivial solutions of the two-parameter Dirichlet boundary value problem (i), and (ii) is given.