×

zbMATH — the first resource for mathematics

Positive solutions for second-order nonlinear differential equations. (English) Zbl 1101.34022
Summary: We prove the existence of positive solutions to the scalar equation \(y^{\prime\prime}(x)+F(x,y,y^{\prime})\) \(=0\). Applications to semilinear elliptic equations in exterior domains are considered.

MSC:
34C11 Growth and boundedness of solutions to ordinary differential equations
35J60 Nonlinear elliptic equations
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Atkinson, F.V., On second order nonlinear oscillation, Pacific J. math., 5, 643-647, (1955) · Zbl 0065.32001
[2] Bielecki, A., Une remarque sur la méthode de banach – cacciopoli-Tikhonov dans le théorie des équations differentielles ordinares, Bull. acad. polon. sci., 4, 261-264, (1956) · Zbl 0070.08103
[3] Constantin, A., Stability of solution sets of differential equations with multivalued right-hand-side, J. differential equations, 114, 243-252, (1994) · Zbl 0808.34013
[4] Constantin, A., Global existence of solutions for perturbed differential equations, Annali mat. pura. appl., 168, 237-299, (1995)
[5] Constantin, A., Existence of positive solutions of quasilinear elliptic equations, Bull. austral. math. soc., 54, 147-154, (1996) · Zbl 0878.35040
[6] Constantin, A., Positive solutions of quasilinear elliptic equations, J. math. anal. appl., 213, 334-339, (1997) · Zbl 0891.35033
[7] Dubé, S.G.; Mingarelli, A.B., Note on a non-oscillation theorem or atkinson, Electron. J. differential equations, 22, 1-6, (2004) · Zbl 1058.34035
[8] Fraenkel, L.E., An introduction to maximum principles and symmetry in elliptic problems, (2000), Cambridge University Press Cambridge · Zbl 0947.35002
[9] Lipovan, O., On the asymptotic behaviour of the solutions to a class of second order nonlinear differential equations, Glasgow math. J., 45, 179-187, (2003) · Zbl 1037.34041
[10] Mustafa, O.; Rogovchenko, Y., Global existence of solutions with prescribed asymptotic behavior for second-order nonlinear differential equations, Nonlinear anal., 51, 339-368, (2002) · Zbl 1017.34005
[11] Noussair, E.S.; Swanson, C.A., Positive solutions of quasilinear elliptic equations in exterior domains, J. math. anal. appl., 75, 121-133, (1980) · Zbl 0452.35039
[12] Rogovchenko, S.; Rogovchenko, Y., Asymptotic behavior of certain second order nonlinear differential equations, Dyn. systems appl., 10, 185-200, (2001) · Zbl 0997.34037
[13] Sugie, J.; Yamaoka, N., Applications of phase plane analysis of a lienard system to positive solutions of Schrödinger equations, Proc. am. math. soc., 131, 501-509, (2002) · Zbl 1107.35050
[14] Wahlén, E., Positive solutions of second-order differential equations, Nonlinear anal., 58, 359-366, (2004) · Zbl 1052.34043
[15] Yin, Z., Monotone positive solutions of second-order nonlinear differential equations, Nonlinear anal., 54, 391-403, (2003) · Zbl 1034.34045
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.