Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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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
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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.

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References

  1. Positive solutions of differential, difference, integral equations R.P.Agarwal;P.J.Y.Wong;D.O'Regan
  2. Math. Sci. Res. Hot-Line v.2 Existence of multiple positive solutions to a conjugate boundary value problem R.I.Avery
  3. Applied Matematics Letters v.13 Three symmetric positive solutions for a second-order boundary value problem R.I.Avery;J.Henderson
  4. 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
  5. Comm. Appl. Nonlinear Anal. v.8 Twin Positive fixed points of nonlinear operators on ordered Banach spaces R.I.Avery;J.Henderson
  6. 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
  7. 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
  8. 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
  9. 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
  10. 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
  11. 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
  12. 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
  13. Computers Math. Applic. v.37 Existence of positive solutions for boundary value problem of second-order FDE P.Weng;D.Jiang