On the solvability of some discontinuous functional impulsive problems

First-order periodic coupled systems with generalized impulse conditions

“…Furthermore, results on equi-regulated functions are essential to deal with the discontinuities at the instants of impulse. A similar problem is studied in [19,20,21], and with similar techniques in [18,22].…”

Differential equations involving homeomorphism with nonlinear boundary conditions

“…An interesting class of nonlinear boundary conditions $$$$ g\left(u(a),{u}^{\prime }(a)\right)=0,\kern0.30em h\left(u(b),{u}^{\prime }(b)\right)=0 $$$$ was considered in Bernfeld and Lakshmikantham 5 . Problems with nonlinear boundary conditions of the type () can be found, for example, in other works, 6–10 where authors investigate these problems using the method of lower and upper solutions, fixed point theorems, and topological degree properties.…”

“…[1][2][3][4] An interesting class of nonlinear boundary conditions g(u(a), u ′ (a)) = 0, h(u(b), u ′ (b)) = 0 ( 7 ) was considered in Bernfeld and Lakshmikantham. 5 Problems with nonlinear boundary conditions of the type (7) can be found, for example, in other works, [6][7][8][9][10] where authors investigate these problems using the method of lower and upper solutions, fixed point theorems, and topological degree properties.…”