in this paper, using the fixed point theory in cone metric spaces, we prove the existence of a unique solution to a first-order ordinary differential equation with periodic boundary conditions in banach spaces admitting the existence of a lower solution.

Lie group analysis is applied to a mathematical model for thin liquid films, namely nonlinear fourth order partial differential equation in two independent variables. A three-dimensional symmetry algebra found and reductions ordinary equations are obtained by using its one-dimensional subalgebras. Two of these studied the reduction method Jacobi last multiplier method, be linearizable. Furtherm...

We consider the boundedness solutions of a certain fourth-order nonlinear and nonhomogeneous differential equation. prove that this equation are bounded byCauchy formula