Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
권호 표지
DOI QR코드

DOI QR Code

A MULTIPLICITY RESULT FOR FOURTH-ORDER BOUNDARY VALUE PROBLEMS VIA CRITICAL POINTS THEOREM

  • Zou, Yu-Mei (Department of Statistics and Finance, College of Information Science and Engineering, Shandong University of Science and Technology)
  • Received : 2010.11.13
  • Accepted : 2011.01.17
  • Published : 2011.09.30
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, using B.Ricceri's three critical points theorem, we prove the existence of at least three classical solutions for the problem $$\{u^{(4)}(t)={\lambda}f(t,\;u(t)),\;t{\in}(0,\;1),\\u(0)=u(1)=u^{\prime}(0)=u^{\prime}(1)=0,$$ under appropriate hypotheses.

Keywords

References

  1. R.P.Agarwal and Y.M.Chow, Iterative methods for a fourth order boundary value problem, Journal of Computational and Applied Mathematics, 10(2)(1984):203-217. https://doi.org/10.1016/0377-0427(84)90058-X
  2. R. Ma and H. Wu, Positive solutions of a fourth-order two-point boundary value problem, Acta Math. Sci. Ser. , A 22(2)(2002):244-249
  3. R. Ma and C. C. Tisdel, Positive solutions of singular sublinear fourth-order boundary value problem, Appl. Anal., 84(2005):1199-1221. https://doi.org/10.1080/00036810500047634
  4. Q. Yao, Solvability of an elastic beam equation with Caratheodory function, Mathematica Applicata, 17(3)(2004):389-392. https://doi.org/10.3969/j.issn.1001-9847.2004.03.012
  5. Q. Yao, Positive solutions for eigenvalue problems of fourth-order elastic beam equations, Appl. Math. Lett, 17(2) (2004):237-243. https://doi.org/10.1016/S0893-9659(04)90037-7
  6. P. Korman, Uniqueness and exact multiplicity of solutions for a class of fourth-order semilinear problems, Proc. Roy. Soc. Edinburgh Sect. A, 134(1)(2004):179-190. https://doi.org/10.1017/S0308210500003140
  7. B. Ricceri,On a three critical points theorem, Arch. Math. 75(2000):220-226. https://doi.org/10.1007/s000130050496
  8. G. Bonanno,Existence of three solutions for a two point boundary value problem, Appl. Math. Lett. 13(2000):53-57.
  9. P. Candito, Existence of three solutions for a nonautonomous two point boundary value problem, J. Math. Anal. Appl.252(2000):532-537. https://doi.org/10.1006/jmaa.2000.6909
  10. X.M. He,W.G. Ge,Existence of three solutions for a quasilinear two-point boundary value problem, Comput. Math. Appl. 45(2003):765-769. https://doi.org/10.1016/S0898-1221(03)00037-3
  11. B. Ricceri, Existence of three solutions for a class of elliptic eigenvalue problems, Math. Comput. Modell. 32(2000):1485-1494. https://doi.org/10.1016/S0895-7177(00)00220-X