The positive properties of Green's function for fractional differential equations and its applications
Summary: We consider the properties of Green's function for the nonlinear fractional differential equation boundary value problem: \(\mathbf{D}^\alpha_{0+}u(t) + f(t, u(t)) + e(t) = 0, 0 < t < 1, u(0) = u'(0) = \cdots = u^{(n-2)}(0) = 0, u(1) = \beta u(\eta)\), where \(n - 1 < \alpha \leq n, n \geq 3, 0 < \beta \leq 1, 0 \leq \eta \leq 1, \mathbf{D}^\alpha_{0+}\) is the standard Riemann-Liouville derivative. Here our nonlinearity \(f\) may be singular at \(u = 0\). As applications of Green's function, we give some multiple positive solutions for singular boundary value problems by means of Schauder fixed-point theorem.
scientific article; zbMATH DE number 6161347
scientific article