Necessary conditions and sufficient conditions for disfocality and disconjugacy of a differential equation.

previous :: next

Necessary conditions and sufficient conditions for disfocality and disconjugacy of a differential equation.

Uri Elias

Source: Pacific J. Math. Volume 81, Number 2 (1979), 379-397.

First Page: Show

Primary Subjects: 34C10

Full-text: Open access

PDF File (1508 KB)
DjVu File (364 KB)

Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.pjm/1102785281
Zentralblatt MATH identifier: 0407.34031
Zentralblatt MATH identifier: 0378.34027
Mathematical Reviews number (MathSciNet): MR547606

back to Table of Contents

References

[1] U. Elias, Oscillatory solutions and extremal points for a linear differentialequation, Arch. Rat. Mech. Anal., to appear,

Mathematical Reviews (MathSciNet): MR81c:34027

Zentralblatt MATH: 0412.34016

[2] G. J. Etgen and C. D. Shih, Disconjugacyof third order differentialequations with nonnegative coefficients, J. Math. Anal. Appl., 41 (1973), 420-425.

Mathematical Reviews (MathSciNet): MR47:3754

Zentralblatt MATH: 0275.34030

[3] R. D. Gentry and C. C. Travis, Comparison of eigenvalues associated withlinear differential equations of arbitrary order, Trans. Amer. Math. Soc, 223 (1976), 167-179.

Mathematical Reviews (MathSciNet): MR54:13198

Zentralblatt MATH: 0339.34012

[4] R. Grimmer, Comparison theorems for third and fourthorder linearequations, J.Differential Equations, 25 (1977), 1-10.

Mathematical Reviews (MathSciNet): MR56:12409

Zentralblatt MATH: 0392.34016

[5] R. Hadass, On the zeros of the solutions of the differential equation y(n) + py =0, Pacific J. Math., 31 (1969), 33-46.

Mathematical Reviews (MathSciNet): MR40:5974

Zentralblatt MATH: 0266.34037

[6] H. Howard, Oscillation criteria for fourthorder linear differentialequations, Trans. Amer. Math. Soc, 96 (1960), 296-311.

Mathematical Reviews (MathSciNet): MR22:8159

Zentralblatt MATH: 0094.28503

[7] I. T. Kiguradze, Oscillation properties of solutions of certain ordinarydifferential equations, Soviet Math. Dokl., 3 (1962), 649-652.

Zentralblatt MATH: 0144.11201

[8] W. J. Kim, On the zeros of the solutions of y(n) + py = 0, J. Math. Anal. Appl., 25 (1969), 189-208.

Mathematical Reviews (MathSciNet): MR40:451

Zentralblatt MATH: 0186.41101

[9] V. A. Kondratev, Oscillatory properties of solutions of the equation y{n) + py -- 0, Trudy. Moskov. Mat. Obsc, 10 (1961), 419-436.

[10] A. C. Lazer, The behavior of solutions of differential equation ytfr -Vpyf 4-qy -- 0, Pacific J. Math., 19 (1966), 435-466.

Mathematical Reviews (MathSciNet): MR33:1552

[11] A. Ju. Levin, A Fredholm equation with a smooth kernel and boundaryvalue problems for a linear differential equation, Soviet Math. Dokl., 5 (1964), 1415-1419.

Mathematical Reviews (MathSciNet): MR29:6266

[12] D. L. Lovelady, Oscillation and a class of odd order linear differentialequations, Hiroshima Math. J., 5 (1975), 371-383.

Mathematical Reviews (MathSciNet): MR52:8561

Zentralblatt MATH: 0334.34043

[13] D. L. Lovelady,Oscillation and even order linear differential equations, Rocky Mountain Math. J., 6 (1976), 299-304.

Mathematical Reviews (MathSciNet): MR52:11196

Zentralblatt MATH: 0335.34019

[14] Z. Nehari, Oscillation criteria for second order linear differentialequations, Trans. Amer. Math. Soc, 85 (1957), 428-445.

Mathematical Reviews (MathSciNet): MR19:415a

Zentralblatt MATH: 0078.07602

[15] Z. Nehari, Non oscillation criteria for nth order linear differential equation, Duke J. Math., 32 (1965), 607-616.

Mathematical Reviews (MathSciNet): MR32:4338

Zentralblatt MATH: 0134.07301

[16] Z. Nehari, Disconjugate linear differential operators, Trans. Amer. Math. Soc, 129 (1967), 500-516.

Mathematical Reviews (MathSciNet): MR36:2860

Zentralblatt MATH: 0183.09101

[17] Z. Nehari, Nonlinear techniques for linear oscillation problems, Trans. Amer. Math. Soc, 210 (1975), 387-406.

Mathematical Reviews (MathSciNet): MR51:8543

Zentralblatt MATH: 0314.34040

[18] Z. Nehari, Green's functions and disconjugacy, Arch. Rat. Mech. Anal., &2 (1976), 53-76.

Mathematical Reviews (MathSciNet): MR54:642

Zentralblatt MATH: 0339.34036

[19] W. Simons, Some disconjugacy criteria for self adjoint linear differentialequa- tions, J. Math. Anal., 34 (1971), 445-463.

Mathematical Reviews (MathSciNet): MR44:521

Zentralblatt MATH: 0219.34036

[20] C. C. Travis, Comparison of eigenvalues for linear differential equations of order

[2n] Trans. Amer. Math. Soc, 177 (1973), 363-374.

Mathematical Reviews (MathSciNet): MR47:5356

Zentralblatt MATH: 0272.34033

previous :: next

Pacific Journal of Mathematics

Credits

Turn MathJax Off
What is MathJax?