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3 Convergence to Zero Conditions for the Solutions
Equations with Degenerate Kernels
3 other sections not shown
approximation is uniformly argument similar assume the kernel Banach space boundedness Cauchy problem continuous function convergente to zero Corollaries and Consequences Degenerate Kernels Differential Equations du)ds equations with degenerate equivalent with g exists a function following conditions following estimation function f satisfies fundamental matrix Further,we shall suppose G of integral holds,then the nonnegative holds,then the trivial holds,then there exists integral inequation 1.1 Lemma of estimation Let now suppose Let suppose lim U(t llowing lx(t nonnegative continuous solutions number of Corollaries omit the details orems proof follows proof is evident relation H relation L-f relation S-U result is embodied satisf:es satisfied,we satisfies the relation solution of 1.1 solution of A;f solution of Cauchy Solutions of Differential tfrC theorem is proved TIMIŞOARA tion trivial solution uniformly asymptotically stable uniformly bounded uniformly convergent uniformly convergente uniformly stable valid,then the nonnegative verifies the relation Volterra Integral Equations zero to infinite