New results and applications on the existence results for nonlinear coupled systems

Talib I., Abdeljawad T., Alqudah M. A., Tunç C., Ameen R.

ADVANCES IN DIFFERENCE EQUATIONS, vol.2021, no.1, 2021 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 2021 Issue: 1
  • Publication Date: 2021
  • Doi Number: 10.1186/s13662-021-03526-2
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Keywords: Fully nonlinear coupled mass-spring model, Generalized nonlinear coupled boundary conditions, Lower and upper solutions approach, Dirichlet boundary conditions, Neumann boundary conditions, BOUNDARY-VALUE-PROBLEMS, ELLIPTIC-SYSTEMS, RADIAL SOLUTIONS, EQUATIONS
  • Van Yüzüncü Yıl University Affiliated: Yes


In this manuscript, we study a certain classical second-order fully nonlinear coupled system with generalized nonlinear coupled boundary conditions satisfying the monotone assumptions. Our new results unify the existence criteria of certain linear and nonlinear boundary value problems (BVPs) that have been previously studied on a case-by-case basis; for example, Dirichlet and Neumann are special cases. The common feature is that the solution of each BVPs lies in a sector defined by well-ordered coupled lower and upper solutions. The tools we use are the coupled lower and upper solutions approach along with some results of fixed point theory. By means of the coupled lower and upper solutions approach, the considered BVPs are logically modified to new problems, known as modified BVPs. The solution of the modified BVPs leads to the solution of the original BVPs. In our case, we only require the Nagumo condition to get a priori bound on the derivatives of the solution function. Further, we extend the results presented in (Franco et al. in Extr. Math. 18(2):153-160, 2003; Franco et al. in Appl. Math. Comput. 153:793-802, 2004; Franco and O'Regan in Arch. Inequal. Appl. 1:423-430, 2003; Asif et al. in Bound. Value Probl. 2015:134, 2015). Finally, as an application, we consider the fully nonlinear coupled mass-spring model.