Existence of Three Solutions for a Class of Two-Point Boundary Value Systems


Affiliations

  • University of Mazandaran, Department of Mathematics, Faculty of Mathematical Sciences, Babolsar, Iran, Islamic Republic of
  • Islamic Azad University, Department of Mathematics, Ghaemshahr, Iran, Islamic Republic of

Abstract

In this paper we prove the existence of an open interval [λ', λ"] for each λ of which a class of two-point boundary value equations depending on λ admits at least three solutions. Our main tool is a recent three critical points theorem of Averna and Bonanno.

Keywords

Three Solutions, Critical Points, Two-Point Boundary Value System.

Subject Discipline

Mathematical Sciences

Full Text:

References

G. A. Afrouzi and A. Hadjian, Infinitely many weak solutions for a class of two-point boundary value systems, J. Nonlinear Analysis and Application, 2012 (2012), Article ID jnaa-00122, 8 Pages.

G. A. Afrouzi, A. Hadjian and S. Heidarkhani, Multiplicity results for a class of twopoint boundary value systems investigated via variational methods, Bull. Math. Soc. Sci.

Math. Roumanie, 55 (2012), 343–352.

G. A. Afrouzi, A. Hadjian and S. Heidarkhani,Non-trivial solutions for a two-point boundary value problem, Ann. Polon. Math., 108 (2013), 75–84.

G. Anello, G. Cordaro, An existence theorem for the Neumann problem involving the p-Laplacian, J. Convex Anal., 10 (2003), 185–198.

D. Averna, G. Bonanno, A three critical points theorem and its applications to the ordinary Dirichlet problem, Topol. Methods Nonlinear Anal., 22 (2003) 93–103.

J. R. Graef, L. Kong, Existence of solutions for nonlinear boundary value problems, Comm. Appl. Nonlinear Anal., 14 (2007) 39–60.

S. Heidarkhani, D. Motreanu, Multiplicity results for a two-point boundary value problem, Panamer. Math. J., 19(3) (2009) 69–78.

S. Heidarkhani, Y. Tian, Multiplicity results for a class of gradient systems depending on two parameters, Nonlinear Anal., 73 (2010) 547–554.

R. Livrea, Existence of three solutions for a quasilinear two point boundary value problem, Arch. Math., 79 (2002) 288–298.

B. Ricceri, On a three critical points theorem, Arch. Math. (Basel), 75 (2000) 220–226.

E. Zeidler, Nonlinear Functional Analysis and its Applications, Vol. II/B, BerlinHeidelberg-New York, 1990.


Refbacks

  • There are currently no refbacks.