Positive solution of fourth-order integral boundary value problem with two parameters (Q638142)

Summary: The author investigates the fourth-order integral boundary value problem with two parameters \[ u^{(4)}(t) + {\beta}u''(t) - {\alpha}u(t) = f(t, u),\quad t \in (0, 1), \] \[ u(0) = u(1) = 0, \quad u''(0) = \int_0^1 u(s) \phi_1 (s)\,ds, \quad u''(1) = \int^1_ 0 u(s) \phi_2 (s)\,ds, \] where the nonlinear term function \(f\) is allowed to change sign. Applying the fixed point index theorem on a cone together with the operator spectrum theorem, some results on the existence of positive solution are obtained.