Abstract
In this paper, we introduce new conditions to prove that the existence and boundedness of the solution by convergent sequences and convergent series. The theorem of Krasnoselskii, Lebesgue’s dominated convergence theorem and fixed point theorem are used to get some sufficient conditions for the existence of solutions. Furthermore, we get sufficient conditions to guarantee the oscillatory property for all solutions in this class of equations. An illustrative example is included as an application to the main results.
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