• 대한수학회보
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• 제49권6호
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• pp.1263-1274
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• 2012

In the present paper we establish some new Opial-type inequalities involving higher order partial derivatives. The results in special cases yield some of the recent results on Opial's inequality and provide new estimates on inequalities of this type.

• Korean Journal of Mathematics
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• 제28권4호
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• pp.717-737
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• 2020

In this paper, we establish some weighted generalization of Opial type inequalities in two independent variables for two functions. We also obtain weighted Opial type inequalities by using p-norms. Special cases of our results reduce to the inequalities in earlier study.

• Kyungpook Mathematical Journal
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• 제51권2호
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• pp.165-175
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• 2011

The purpose of this note is to give Opial type inequalities with nonlocal conditions. Also, a reverse of the original inequality with y(a) = y(b) = 0 is derived. We apply these inequalities to second-order differential equations with nonlocal conditions to derive several necessary conditions for the existence of solutions.