Optimal Existence Conditions for the Periodic Delay ϕ-Laplace Equation with upper and lower Solutions in the Reverse order

Homoclinic Solutions for a Class of the Second-Order Impulsive Hamiltonian Systems

“…Izydorek and Janczewska [2] studied the existence of homoclinic solutions of it. Some classical tools such as some fixed point theorems in cones, topological degree theory, the upper and lower solutions method combined with monotone iterative technique, and variational methods [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] have been widely used to get solutions of impulsive differential equations. However, the existence of homoclinic solutions for the impulsive systems is paid little attention.…”