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Existence Results for a 2nth-Order Differential Equation with Sturm-Liouville Operator

Abstract Critical point results for a 2nth-order differential equation with Sturm-liouville operator is exploited in order to prove that a suitable class possesses at least one solution under an asymptotical behavior of the potential of the nonlinear term at zero, and also possesses infinitely many solutions under some hypotheses on the behavior of the potential of the nonlinear term at infinity. Some recent results are extended and improved. Some examples are included to dwell upon the usefulness of the results obtained.