Impulsive boundary value problems with integral boundary conditions and one-dimensional \(p\)-Laplacian
The authors consider the impulsive boundary value problem of second order with \(p\)-Laplacian \[ \begin{aligned} &-(\varphi_p(u'(t)))' = f(t,u(t)),\quad t \in (0,1)\setminus\{t_1,\dots,t_m\},\\ &-\triangle u|_{t=t_k} = I_k(u(t_k)), \quad k = 1,\dots,m,\\ &u'(0) = 0, \quad u(1) = \int_0^1 g(t)u(t) \,dt, \end{aligned} \] where \(0 < t_1 < \dots < t_m < 1\) are impulse points, \(f\), \(I_k\) are continuous, \(g\) is integrable on \([0,1]\) and nonnegative. Sufficient conditions ensuring the existence of at least two positive solutions of the BVP are obtained. The proofs are based on fixed point theorem in cones.
scientific article; zbMATH DE number 5539191
scientific article