Problems with Mean Curvature-Like Operators and Three-Point Boundary Conditions

  • Dionicio Pastor Dallos SantosEmail author


In this paper we study the existence of solutions for a new class of nonlinear differential equations with three-point boundary conditions. Existence of solutions are obtained by using the Leray–Schauder degree.


Boundary value problems Leray–Schauder degree Mean curvature-like operators 

Mathematics Subject Classification

34B15 47H11 



This research was supported by CAPES and CNPq/Brazil. The author would like to thank to Dr. Pierluigi Benevieri for his kind advice and for the constructive revision of this paper.

Compliance with ethical standards

Conflict of interest

The author declares that there is no conflict of interest regarding the publication of this article.


  1. Bereanu, C., Mawhin, J.: Boundary value problems for some nonlinear systems with singular \(\varphi \)-laplacian. J. Fixed Point Theory Appl. 4, 57–75 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  2. Benevieri, P., do Ó, J.M., Souto de Medeiros, E.: Periodic solutions for nonlinear systems with mean curvature-like operators. Nonlinear Anal. 65, 1462–1475 (2006)Google Scholar
  3. Bereanu, C., Mawhin, J.: Existence and multiplicity results for some nonlinear problems with singular \(\varphi \)-laplacian. J. Differ. Equ. 243, 536–557 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  4. Bereanu, C., Mawhin, J.: Boundary-value problems with non-surjective \(\varphi \)-laplacian and one-sided bounded nonlinearity. Adv. Differ. Equ. 11, 35–60 (2006)MathSciNetzbMATHGoogle Scholar
  5. Bonheure, D., Habets, P., Obersnel, F., Omari, P.: Classical and non-classical solutions of a prescribed curvature equation. J. Differ. Equ. 243, 208–237 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  6. Bonheure, D., Habets, P., Obersnel, F., Omari, P.: Classical and non-classical solutions of a prescribed curvature equation with singularities. Rend. Istit. Mat. Univ. Trieste. 32, 1–22 (2007)MathSciNetzbMATHGoogle Scholar
  7. Brubaker, N.D., Pelesko, J.A.: Analysis of a one-dimensional prescribed mean curvature equation with singular nonlinearity. Nonlinear Anal. 75, 5086–5102 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  8. Deimling, K.: Nonlinear Functional Analysis. Springer, Berlin (1985)CrossRefzbMATHGoogle Scholar
  9. Li, W.S., Liu, Z.L.: Exact number of solutions of a prescribed mean curvature equation. J. Math. Anal. Appl. 367, 486–498 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  10. Mawhin, J.: Leray-Schauder degree: a half century of extensions and applications. Topol. Methods Nonlinear Anal. 14, 195–228 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  11. Santos, D.P.D.: Existence of solutions for some nonlinear problems with boundary value conditions. Abstr. Appl. Anal. (2016). doi: 10.1155/2016/5283263

Copyright information

© Sociedade Brasileira de Matemática 2017

Authors and Affiliations

  1. 1.Department of MathematicsIME-USP, Cidade UniversitáriaSão PauloBrazil

Personalised recommendations