Behaviour of solutions of a fourth-order self-adjoint linear differential equation

Švec, Marko

doi:10.4064/ap-42-1-333-344

Cited by 3 publications

(2 citation statements)

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“…are integers of admissible parities. Some of their useful properties are now summarised: For various applications of S(y, x + ) see, for example, [5][6][7]12]. Now we define a basis for the solution space of equation (1.1) by means of boundary value problems.…”

Section: L N Y(z))mentioning

confidence: 99%

Minors of the Wronskian of the differential equation L_ny + p(x)y = 0. II. Dominance of solutions

Elias

1988

Proceedings of the Royal Society of Edinburgh: Section A Mathem

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SynopsisThe equation studied here is Lny + p(x)y = 0, where Ln is a disconjugate differential operator and p(x) is of a fixed sign. We define a basis of the solution space and order its elements according to their relative magnitudes near infinity. Our method is independent of the possible oscillation or nonoscillation of the solutions and it is achieved by utilising the fact that some minors of the Wronskian never vanish.

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Section: L N Y(z))mentioning

confidence: 99%

Minors of the Wronskian of the differential equation L_ny + p(x)y = 0. II. Dominance of solutions

Elias

1988

Proceedings of the Royal Society of Edinburgh: Section A Mathem

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“…The application of S(y, x + ) seems to be a useful method to investigate (1.1). See for example [4,5,10]. We list here several properties of S(y, x + ), S(y, x~).…”

Section: L N Y( §))mentioning

confidence: 99%

Minors of the wronskian of the differential equation L_ny+p(x)y=0

Elias¹

1987

Proceedings of the Royal Society of Edinburgh: Section A Mathem

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SynopsisThe equation studied here is Lny +p(x)y = 0, where Ln is a disconjugate differential operator and p(x) is of a fixed sign. It is shown that certain minors of the wronskian of this equation satisfy a very similar differential equation Mnz +p(x)z =0. We prove that some properties of the original equation which are essential for oscillation theory are inherited by the solutions of the second one.

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A classification of the solutions of a difference equation according to their behavior at infinity

Hankerson

Peterson

1988

Journal of Mathematical Analysis and Applications

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Behaviour of solutions of a fourth-order self-adjoint linear differential equation

Cited by 3 publications

References 0 publications

Minors of the Wronskian of the differential equation L_ny + p(x)y = 0. II. Dominance of solutions

Minors of the Wronskian of the differential equation L_ny + p(x)y = 0. II. Dominance of solutions

Minors of the wronskian of the differential equation L_ny+p(x)y=0

A classification of the solutions of a difference equation according to their behavior at infinity

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Behaviour of solutions of a fourth-order self-adjoint linear differential equation

Cited by 3 publications

References 0 publications

Minors of the Wronskian of the differential equation Lny + p(x)y = 0. II. Dominance of solutions

Minors of the Wronskian of the differential equation Lny + p(x)y = 0. II. Dominance of solutions

Minors of the wronskian of the differential equation Lny+p(x)y=0

A classification of the solutions of a difference equation according to their behavior at infinity

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Product

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About

Minors of the Wronskian of the differential equation L_ny + p(x)y = 0. II. Dominance of solutions

Minors of the Wronskian of the differential equation L_ny + p(x)y = 0. II. Dominance of solutions

Minors of the wronskian of the differential equation L_ny+p(x)y=0