Sentence examples for unbounded term from inspiring English sources

We study Hamilton-Jacobi equations with an unbounded term in Hilbert spaces.

The following lemma gives an exponential inequality for the sum of unbounded terms.

We study the Hamilton-Jacobi equation of a system governed either by a "semilinear" or by a "monotone" dynamics, replacing the unbounded terms of this equation by their Yosida approximations.

In order to make full use of A3 and the unbounded terms in the coefficients of system (1), take (sqrt{delta ( t )} Vert x ( t ) Vert ), (sqrt{ ( 1-alpha ){{lambda}_{min}} ( G )}Vert x ( t-tau ( t ) ) Vert ) and (sqrt{rho ( t )}vert f ( sigma{ ( t )} ) vert ) as the following variables of the quadratic form.

end{aligned} In order to take advantage of A5 and the unbounded terms in the coefficients of system (4), let us take (sqrt{delta ( t )}Vert x ( t ) Vert ), (sqrt{ ( 1-alpha ){{lambda}_{min}} ( G )}Vert x ( t-tau ( t ) ) Vert ) and (sqrt{{{rho}_{i}} ( t )}vert {{f}_{i}} ( {{sigma}_{i}{ ( t )}} ) vert ) ((i=1,2,ldots,m)) as the following variables of the quadratic form.

end{aligned} end{aligned} To fully utilize A3, A4, and the unbounded terms in system coefficients, we take (sqrt{{{delta}_{i}} ( t )} Vert {{x}_{i}} ( t ) Vert ), (sqrt{ ( 1-{{alpha}_{i}} ){{lambda}_{min}} ({{G}_{i}} )} Vert x ( t-{{tau}_{i}} ( t ) ) Vert ) ((i=1,2,ldots,m )), and (sqrt{rho ( t )} vert f ( sigma ( t ) ) vert ) as the variables of the following quadratic form.

In certain cases, which include isosceles and right triangles, we obtain the exact value of all the coefficients of the unbounded terms in the asymptotic expansion as the angle opening approaches zero, plus the constant term and estimates on the remainder.

We use the term unbounded to mean doubly infinite (no boundaries of any kind).

In this paper, we have investigated asymptotic properties of solutions for an impulsive neutral differential equation with positive and negative coefficients, unbounded delays, forced term, and constant impulsive jumps.

ARFDEs where the operator acting on delay term is unbounded have been studied in some works.

By variational methods we consider a p-biharmonic equation with nonlocal term on unbounded domain.