Previous |  Up |  Next

Article

Full entry | PDF   (0.2 MB)
Keywords:
half-linear equation; scalar p-Laplacian; conjugate points; conjugacy criteria
Summary:
Sufficient conditions on the function $c(t)$ ensuring that the half-linear second order differential equation $(|u^\prime |^{p-2} u^\prime )^\prime + c(t)|u(t)|^{p-2} u(t)=0\,, \quad \quad p>1$ possesses a nontrivial solution having at least two zeros in a given interval are obtained. These conditions extend some recently proved conjugacy criteria for linear equations which correspond to the case $p=2$.
References:
[1] Došlý, O.: Conjugacy criteria for second order differential equations. Rocky Mountain, J. Math. 23(1993), 849-861. MR 1245450
[2] Elbert, Á.: A half-linear second order differential equation. Colloquia Math. Soc. Janos Bolyai, 30, Qualitative theory of differential equation, Szeged (1979), 153-180. MR 0680591 | Zbl 0511.34006
[3] Harris, B. J., Kong, Q.: On the oscillation of differential equations with an oscillatory coefficient. Trans. Amer. Math. Soc. 347(1995), 1831-1839. MR 1283552
[4] Li, H. J., Yeh, C. Ch.: Oscillations of half-linear second order differential equations. Hiroshima Math. J. 25(1995), 585-594. MR 1364076
[5] Müller-Pfeiffer, E.: Existence of conjugate points for second and fourth order differential equations. Proc. Roy. Soc. Edinburgh Sect. A 89(1981), 281-291. MR 0635764
[6] Tipler, F. J.: General relativity and conjugate ordinary differential equations. J. Diff. Equations 30(1978), 165-174. MR 0513268 | Zbl 0362.34023

Partner of