Displaying 481 – 500 of 933

Showing per page

On singularly perturbed ordinary differential equations with measure-valued limits

Zvi Artstein (2002)

Mathematica Bohemica

The limit behaviour of solutions of a singularly perturbed system is examined in the case where the fast flow need not converge to a stationary point. The topological convergence as well as information about the distribution of the values of the solutions can be determined in the case that the support of the limit invariant measure of the fast flow is an asymptotically stable attractor.

On small solutions of second order differential equations with random coefficients

László Hatvani, László Stachó (1998)

Archivum Mathematicum

We consider the equation x ' ' + a 2 ( t ) x = 0 , a ( t ) : = a k if t k - 1 t < t k , for k = 1 , 2 , ... , where { a k } is a given increasing sequence of positive numbers, and { t k } is chosen at random so that { t k - t k - 1 } are totally independent random variables uniformly distributed on interval [ 0 , 1 ] . We determine the probability of the event that all solutions of the equation tend to zero as t .

On some boundary value problems for second order nonlinear differential equations

Zuzana Došlá, Mauro Marini, Serena Matucci (2012)

Mathematica Bohemica

We investigate two boundary value problems for the second order differential equation with p -Laplacian ( a ( t ) Φ p ( x ' ) ) ' = b ( t ) F ( x ) , t I = [ 0 , ) , where a , b are continuous positive functions on I . We give necessary and sufficient conditions which guarantee the existence of a unique (or at least one) positive solution, satisfying one of the following two boundary conditions: i ) x ( 0 ) = c > 0 , lim t x ( t ) = 0 ; ii ) x ' ( 0 ) = d < 0 , lim t x ( t ) = 0 .

On some properties of the solution of the differential equation u ' ' + 2 u ' r = u - u 3

Valter Šeda, Ján Pekár (1990)

Aplikace matematiky

In the paper it is shown that each solution u ( r , α ) ot the initial value problem (2), (3) has a finite limit for r , and an asymptotic formula for the nontrivial solution u ( r , α ) tending to 0 is given. Further, the existence of such a solutions is established by examining the number of zeros of two different solutions u ( r , α ¯ ) , u ( r , α ^ ) .

On stable polynomials

Miloslav Nekvinda (1989)

Aplikace matematiky

The article is a survey on problem of the theorem of Hurwitz. The starting point of explanations is Schur's decomposition theorem for polynomials. It is showed how to obtain the well-known criteria on the distribution of roots of polynomials. The theorem on uniqueness of constants in Schur's decomposition seems to be new.

On the asymptotic behavior at infinity of solutions to quasi-linear differential equations

Irina Astashova (2010)

Mathematica Bohemica

Sufficient conditions are formulated for existence of non-oscillatory solutions to the equation y ( n ) + j = 0 n - 1 a j ( x ) y ( j ) + p ( x ) | y | k sgn y = 0 with n 1 , real (not necessarily natural) k > 1 , and continuous functions p ( x ) and a j ( x ) defined in a neighborhood of + . For this equation with positive potential p ( x ) a criterion is formulated for existence of non-oscillatory solutions with non-zero limit at infinity. In the case of even order, a criterion is obtained for all solutions of this equation at infinity to be oscillatory. Sufficient conditions are obtained...

Currently displaying 481 – 500 of 933