  This paper is devoted to prove the existence of one or multiple solutions of
a wide range of nonlinear differential boundary value problems.
  To this end, we obtain some new fixed point theorems for a class of integral
operators. We follow the well-known Krasnoselski\u{\i}'s fixed point Theorem
together with two fixed point results of Leggett-Williams type.
  After obtaining a general existence result for a one parameter family of
nonlinear differential equations, are proved, as particular cases, existence
results for second and fourth order nonlinear boundary value problems.
