Nontrivial solutions for a class of fractional differential equations with integral boundary conditions and a parameter in a Banach space with lattice
Summary: Existence of nontrivial solutions for the following fractional differential equation with integral boundary conditions \(D^\alpha_{0+}u(t) + h(t)f(t, u(t)) = 0\), \(0 < t < 1\), \(u(0) = u'(0) = u''(0) = 0\), \(u(1) = \lambda \int^\eta_0 u(s)\text{d}s\) is investigated by using results for the computation of topological degree under the lattice structure, where \(3 < \alpha \leq 4\), \(0 < \eta \leq 1\), \(0 \leq \lambda \eta^\alpha / \alpha < 1\), \(D^\alpha_{0+}\) is the standard Riemann-Liouville derivative. \(h(t)\) is allowed to be singular at \(t = 0\) and \(t = 1\).
scientific article; zbMATH DE number 6134077
scientific article