In this paper we propose a new method to solve integral inequalities of Henry᎐Gronwall type and their Bihari nonlinear version. Nonlinear integral inequalities with weakly singular kernels and with multiple integrals as well as a modification of the Ou᎐Iang᎐Pachpatte inequality are also treated.ᮊ 1997 Academic Press

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A criterion for the nonexplosion of solutions to semilinear evolution equations on Banach spaces is proved. The result is obtained by applying a modification of the Bihari type inequality to the case of a weakly singular nonlinear integral inequality.  2002 Elsevier Science (USA)

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