Multiple solutions of impulsive Sturm-Liouville boundary value problem via lower and upper solutions and variational methods
The authors consider the impulsive Sturm-Liouville boundary value problem \[ \begin{aligned} &-Lu = f(x,u), \quad x \in [0,1]\setminus\{x_1,\dots,x_\ell\},\\ &-\Delta(p(x_i)u'(x_i)) = I_i(u(x_i)), \quad i = 1,\dots,\ell,\\ &R_1(u) = 0, \quad R_2(u) = 0, \end{aligned} \] where \(Lu = (p(x)u')' - q(x)u\) is a Sturm-Liouville operator, \(R_1(u) = \alpha u'(0) - \beta u(0)\), \(R_2(u) = \gamma u'(1) + \sigma u(1)\), \(0 < x_1 < \dots < x_\ell < 1\). Using lower and upper solutions method and variational methods, there is obtained an existence result for at least four solutions of the BVP.
impulsive Sturm-Liouville boundary value problem
scientific article; zbMATH DE number 5994315
scientific article