Nonlinear higher order boundary value problems with multiple positive solutions. (Q1414225)

Motivated by the paper of \textit{J. Henderson and H. B. Thompson} [Commun. Appl. Nonlinear Anal. 7, No. 1, 55--62 (2000; Zbl 1108.34306)], the authors study the existence and multiplicity of solutions for \(n\)th-order boundary value problems of the form \(y^{(n)}(x)+f(y)(x) = 0\), \(x \in [0,1]\); \(y^{(k)}(0) = 0\), \(0 \leq k \leq n-2\), \(y^{(j)}(1) = 0,\) for one fixed \(j\) satisfying \(1 \leq j \leq n-2.\) Here, \(n \geq 2,\) and \(f\) is a nonnegative continuous real function. Given \(n,j \) and \(N,\) they formulate some additional restrictions on the function \(f\) which guarantee the existence of at least \(N\) positive solutions. Shooting methods are used in the proofs.