Oscillation criteria for the sublinear Schrödinger equation

Onose, Hiroshi

doi:10.1090/S0002-9939-1982-0647900-4

Oscillation criteria for the sublinear Schrödinger equation
HTML articles powered by AMS MathViewer

by Hiroshi Onose PDF

Proc. Amer. Math. Soc. 85 (1982), 69-72 Request permission

Abstract:

In this paper, we propose an oscillation theorem to the sublinear Emden-Fowler equation $\Delta u + g(x){u^\gamma } = 0$ for $n = 2$. By using this, we will answer to the open problem of Noussair and Swanson in the case of bounded solutions.

References

W. Allegretto, Oscillation criteria for quasilinear equations, Canadian J. Math. 26 (1974), 931–947. MR 344642, DOI 10.4153/CJM-1974-088-0
Yuichi Kitamura and Takaŝi Kusano, An oscillation theorem for a sublinear Schrödinger equation, Utilitas Math. 14 (1978), 171–175. MR 511522

On the solutions of elliptic equations

Kurt Kreith and Curtis C. Travis, Oscillation criteria for selfadjoint elliptic equations, Pacific J. Math. 41 (1972), 743–753. MR 318642, DOI 10.2140/pjm.1972.41.743
Manabu Naito and Norio Yoshida, Oscillation theorems for semilinear elliptic differential operators, Proc. Roy. Soc. Edinburgh Sect. A 82 (1978/79), no. 1-2, 135–151. MR 524680, DOI 10.1017/S0308210500011112
E. S. Noussair and C. A. Swanson, Oscillation theory for semilinear Schrödinger equations and inequalities, Proc. Roy. Soc. Edinburgh Sect. A 75 (1975/76), no. 1, 67–81. MR 442436, DOI 10.1017/S0080454100012541
E. S. Noussair and C. A. Swanson, Positive solutions of quasilinear elliptic equations in exterior domains, J. Math. Anal. Appl. 75 (1980), no. 1, 121–133. MR 576278, DOI 10.1016/0022-247X(80)90310-8
E. S. Noussair and C. A. Swanson, Oscillation of semilinear elliptic inequalities by Riccati transformations, Canadian J. Math. 32 (1980), no. 4, 908–923. MR 590655, DOI 10.4153/CJM-1980-069-8