Displaying 681 – 700 of 806

Showing per page

Some new oscillation criteria for second order elliptic equations with damping

Rong-Kun Zhuang, Zheng-an Yao (2005)

Annales Polonici Mathematici

Some new oscillation criteria are obtained for second order elliptic differential equations with damping i , j = 1 n D i [ A i j ( x ) D j y ] + i = 1 n b i ( x ) D i y + q ( x ) f ( y ) = 0 , x ∈ Ω, where Ω is an exterior domain in ℝⁿ. These criteria are different from most known ones in the sense that they are based on the information only on a sequence of subdomains of Ω ⊂ ℝⁿ, rather than on the whole exterior domain Ω. Our results are more natural in view of the Sturm Separation Theorem.

Some notes on oscillation of two-dimensional system of difference equations

Zdeněk Opluštil (2014)

Mathematica Bohemica

Oscillatory properties of solutions to the system of first-order linear difference equations Δ u k = q k v k Δ v k = - p k u k + 1 , are studied. It can be regarded as a discrete analogy of the linear Hamiltonian system of differential equations. We establish some new conditions, which provide oscillation of the considered system. Obtained results extend and improve, in certain sense, results presented in Opluštil (2011).

Some oscillation theorems for second order differential equations

Chung-Fen Lee, Cheh Chih Yeh, Chuen-Yu Gau (2005)

Czechoslovak Mathematical Journal

In this paper we establish some oscillation or nonoscillation criteria for the second order half-linear differential equation ( r ( t ) Φ ( u ' ( t ) ) ) ' + c ( t ) Φ ( u ( t ) ) = 0 , where (i) r , c C ( [ t 0 , ) , : = ( - , ) ) and r ( t ) > 0 on [ t 0 , ) for some t 0 0 ; (ii) Φ ( u ) = | u | p - 2 u for some fixed number p > 1 . We also generalize some results of Hille-Wintner, Leighton and Willet.

Some properties of third order differential operators

Mariella Cecchi, Zuzana Došlá, Mauro Marini (1997)

Czechoslovak Mathematical Journal

Consider the third order differential operator L given by L ( · ) 1 a 3 ( t ) d d t 1 a 2 ( t ) d d t 1 a 1 ( t ) d d t ( · ) and the related linear differential equation L ( x ) ( t ) + x ( t ) = 0 . We study the relations between L , its adjoint operator, the canonical representation of L , the operator obtained by a cyclic permutation of coefficients a i , i = 1 , 2 , 3 , in L and the relations between the corresponding equations. We give the commutative diagrams for such equations and show some applications (oscillation, property A).

Spectral properties of fourth order differential operators

Ondřej Došlý, Roman Hilscher (1997)

Mathematica Bohemica

Necessary and sufficient conditions for discreteness and boundedness below of the spectrum of the singular differential operator ( y ) 1 w ( t ) ( r ( t ) y ) , t [ a , ) are established. These conditions are based on a recently proved relationship between spectral properties of and oscillation of a certain associated second order differential equation.

Currently displaying 681 – 700 of 806