ON THE EIGENVALUES OF A NON-LINEAR STURM-LIOUVILLE BOUNDARY VALUE PROBLEM

In the present paper, a boundary value problem consisting of anon-linear Sturm-Liouville equation having a symmetric potential k(t) anda spectral parameter with Dirichlet boundary conditions on the intervalI := (-1; 1) is investigated. For 1 ≤ q < ∞, we obtain the asymptoticformula for the Lq-bifurcation curve λ= λ (q;α) as α→∞.

Keywords:

Non-linear Sturm-Liouville problem , Lq-bifurcation branch , asymptotic representation