Wyniki wyszukiwania

1

On oscillation of solutions of forced nonlinear neutral differential equations of higher order II

100%

Parhi N., Rath R.

Annales Polonici Mathematici

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2003

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tom 81

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nr 2

101-110

EN

Sufficient conditions are obtained so that every solution of $[y(t) - p(t)y(t-τ)]^{(n)} + Q(t)G(y(t-σ)) = f(t)$ where n ≥ 2, p,f ∈ C([0,∞),ℝ), Q ∈ C([0,∞),[0,∞)), G ∈ C(ℝ,ℝ), τ > 0 and σ ≥ 0, oscillates or tends to zero as $t→ ∞ $. Various ranges of p(t) are considered. In order to accommodate sublinear cases, it is assumed that $∫_0^{∞} Q(t)dt = ∞$. Through examples it is shown that if the condition on Q is weakened, then there are sublinear equations whose solutions tend to ±∞ as t → ∞.

2

Oscillation criteria for second order self-adjoint matrix differential equations

100%

Parhi N., Praharaj P.

Annales Polonici Mathematici

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1999

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tom 72

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nr 1

1-14

EN

Some results concerning oscillation of second order self-adjoint matrix differential equations are obtained. These may be regarded as a generalization of results for the corresponding scalar equations.

3

Oscillation criteria for a class of nonlinear differential equations of third order

100%

Parhi N., Das P.

Annales Polonici Mathematici

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1992

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tom 57

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nr 3

219-229

EN

Oscillation criteria are obtained for nonlinear homogeneous third order differential equations of the form $y''' + q(t)y' + p(t)y^α = 0$ and y''' + q(t)y' + p(t)f(y) = 0, where p and q are real-valued continuous functions on [a,∞), f is a real-valued continuous function on (-∞, ∞) and α > 0 is a quotient of odd integers. Sign restrictions are imposed on p(t) and q(t). These results generalize some of the results obtained earlier in this direction.

4

On distance between zeros of solutions of third order differential equations

100%

Parhi N., Panigrahi S.

Annales Polonici Mathematici

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2001

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tom 77

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nr 1

21-38

EN

The lower bounds of the spacings b-a or a'-a of two consecutive zeros or three consecutive zeros of solutions of third order differential equations of the form y''' + q(t)y' + p(t)y = 0 (*) are derived under very general assumptions on p and q. These results are then used to show that $t_{n+1} - tₙ → ∞$ or $t_{n+2} - tₙ → ∞$ as n → ∞ under suitable assumptions on p and q, where ⟨tₙ⟩ is a sequence of zeros of an oscillatory solution of (*). The Opial-type inequalities are used to derive lower bounds of the spacings d-a or b-d for a solution y(t) of (*) with y(a) = 0 = y'(a), y'(c) = 0 and y''(d) = 0 where d ∈ (a,c) or y'(c) = 0, y(b) = 0 = y'(b) and y''(d) = 0 where d ∈ (c,b).

5

Oscillatory behaviour of solutions of forced neutral differential equations

100%

Parhi N., Mohanty P.

Annales Polonici Mathematici

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1996-1997

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tom 65

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nr 1

1-10

EN

Sufficient conditions are obtained for oscillation of all solutions of a class of forced nth order linear and nonlinear neutral delay differential equations. Also, asymptotic behaviour of nonoscillatory solutions of a class of forced first order neutral equations is studied.

6

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On the behaviour of solutions of the differential equations $(r(t)y'')' + q(t)(y')^β + p(t)y^α = f(t)$

100%

Parhi N., Parhi S.

Annales Polonici Mathematici

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1986-1987

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tom 47

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nr 2

137-148

Ograniczanie wyników

6 Annales Polonici Mathematici

6 Parhi N.

1 Das P.

1 Mohanty P.

1 Panigrahi S.

1 Parhi S.

1 Praharaj P.

1 Rath R.

1 2003

1 2001

1 1999

1 1996

1 1992

1 1986

On oscillation of solutions of forced nonlinear neutral differential equations of higher order II

Oscillation criteria for second order self-adjoint matrix differential equations

Oscillation criteria for a class of nonlinear differential equations of third order

On distance between zeros of solutions of third order differential equations

Oscillatory behaviour of solutions of forced neutral differential equations

On the behaviour of solutions of the differential equations $(r(t)y'')' + q(t)(y')^β + p(t)y^α = f(t)$