Boundary-value Problems for the One-dimensional p-Laplacian with Even Superlinearity

Abstract

<p>This paper is concerned with a study of the quasilinear problem</p> <pre>−(|u'|^p−2u')' = |u|^p − λ, in (0, 1),<br> u(0) = u(1) = 0,</pre> <p>where p >1 and λ ∈ ℝ are parameters. For λ > 0, we determine a lower bound for the number of solutions and establish their nodal properties. For λ ≤ 0, we determine the exact number of solutions. In both cases we use a quadrature method.</p>