TWIN POSITIVE SOLUTIONS OF FUNCTIONAL DIFFERENTIAL EQUATIONS FOR THE ONE-DIMENSIONAL ρ-LAPLACIAN

• Bai, Chuan-Zhi (Department of Mathematics, Huaiyin Teacher′s College) ;
• Fang, Jin-Xuan (Department of Mathematics, Hanjing Normal University)
• Published : 2003.05.01

Abstract

For the boundary value problem (BVP) of second order functional differential equations for the one-dimensional $\rho$-Laplaclan: ($\Phi$$_{\rho}$(y'))'(t)+m(t)f(t, $y^{t}$ )=0 for t$\in$[0,1], y(t)=η(t) for t$\in$[-$\sigma$,0], y'(t)=ξ(t) for t$\in$[1,d], suitable conditions are imposed on f(t, $y^{t}$ ) which yield the existence of at least two positive solutions. Our result generalizes the main result of Avery, Chyan and Henderson.

References

1. Computers Math. Applic. v.42 Twin solutions of boundary value problems for ordinary differential equations and finite difference equations R.I.Avery;C.J.Chyan;J.Henderson https://doi.org/10.1016/S0898-1221(01)00188-2
2. Computers Math. Applic. v.37 Existence of positive solutions for boundary value problem of second-order FDE P.Weng;D.Jiang
3. Math. Sci. Res. Hot-Line v.2 Existence of multiple positive solutions to a conjugate boundary value problem R.I.Avery
4. Indiana Univ. Math. J. v.28 Multiple positive fixed-points of nonlinear operators on ordered Banach spaces R.W.Leggett;L.R.Williams https://doi.org/10.1512/iumj.1979.28.28046
5. J. Math. Anal. Appl. v.190 Multiplicity results for the 1-dimensional generalized p-Laplacian R.Ubilla https://doi.org/10.1006/jmaa.1995.1097
6. Computers Math. Applic. v.40 Existence of positive solutions for functional differential equations C.H.Hong;C.C.Yeh;C.F.Lee;F.H.Wong https://doi.org/10.1016/S0898-1221(00)00196-6
7. Proc. Amer. Math. Soc. v.128 Multiple symmetric positive solutions for a second-order boundary value problem J.Handerson;H.B.Thompson https://doi.org/10.1090/S0002-9939-00-05644-6
8. J. Math. Anal. Appl. v.201 A singular boundary value problem for the one dimensional p-Laplacian J.Y.Wang;W.J.Gao https://doi.org/10.1006/jmaa.1996.0288
9. Comm. Appl. Nonlinear Anal. v.8 Twin Positive fixed points of nonlinear operators on ordered Banach spaces R.I.Avery;J.Henderson
10. Positive solutions of differential, difference, integral equations R.P.Agarwal;P.J.Y.Wong;D.O'Regan
11. Proc. Amer. Math. Soc. v.120 On the existence of positive solutions of ordinary differential equations L.H.Erbe;H.Wang https://doi.org/10.1090/S0002-9939-1994-1204373-9
12. Applied Matematics Letters v.13 Three symmetric positive solutions for a second-order boundary value problem R.I.Avery;J.Henderson
13. J. Math. Anal. Appl. v.184 Multiple positive solutions of some boundary value problems L.H.Erbe;S.Hu;H.Wang https://doi.org/10.1006/jmaa.1994.1227