Sentence examples for dynamic inequality from inspiring English sources

If the delay dynamic inequality (2.10).

If (p ( t ) leq0) on ([ a,b ] _{ mathbb{T}}), Y is (Delta_{2,mathrm{gH}} -differentiable on (left.[ a,mathrm{gH}} -differentiablesatisfies the interval dynamic inequality (23) then it satisfies (24).

(b) If (p(t)leq0) on ([ a,b ] _{mathbb {T}}), Y is (Delta_{2,mathrm{gH}} -differentiable on (left.[ a,mathrm{gH}} -differentiablesatisfies the interval dynamic inequality, (9) then (10) honds, for alefttin [ a,b ] _{mathbb{T}}).  .

(b) If (p(t geq0) on ([ a,b ] _{mathbb {T}}), Y is (Delta_{2,mathrm{gH}} -differentiable on (left.[ a,mathrm{gH}} -differentiable satisfies the interval dynamic inequality (17) then (18) honds, for alefttin [ a,b ] _{mathbb{T}}).  .

If there exists a λ ∈ [ 0, 1 ] such that lim inf t → ∞ ∫ τ ( t ) t p ( s ) Δ s > λ and lim sup t → ∞ ∫ τ ( t ) σ ( t ) p ( s ) Δ s > 1 − ( 1 − 1 − λ ) 2, then the delay dynamic inequality (2.1) has no eventually positive solutions.

(a) If (p(t geq0) on ([ a,b ] _{mathbb {T}}), Y is (Delta_{1,mathrm{gH}} -differentiable on (left.[ a,mathrm{gH}} -differentiable satisfies the interval dynamic inequality Y^{Delta} ( t ) leq p ( t ) Y ( t ) quad textit{fon alefttin bigl.[ a,b )bigrightathbb{T}}, (15) then Y ( t ) leq e_{p} ( t,a ) Y ( a ) (16) for all (tin [ a,b ]_{mathbb{T}})._{mathbb{

The following theorem is a foundational result in dynamic inequalities.

The purpose of this paper is to investigate some new dynamic inequalities on time scales.

(2) Using our main results, we can obtain many dynamic inequalities for some peculiar time scales.

By establishing some dynamic inequalities on time scales, a permanence result for the model is obtained.

In Section 3 we deal with our nonlinear dynamic inequalities on time scales with 'maxima'.