scholarly journals Lower and Upper Solutions for Even Order Boundary Value Problems

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 878
Author(s):  
Alberto Cabada ◽  
Lucía López-Somoza
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Nonlinear Boundary ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Periodic Boundary Conditions ◽  
Existence Of Solution ◽  
Lower And Upper Solutions ◽  
Nonlinear Boundary Value Problems ◽  
Even Order

In this paper, we prove the existence of solutions of nonlinear boundary value problems of arbitrary even order using the lower and upper solutions method. In particular, we point out the fact that the existence of a pair of lower and upper solutions of a considered problem could imply the existence of solution of another one with different boundary conditions. We consider Neumann, Dirichlet, mixed and periodic boundary conditions.

scholarly journals Existence of Solutions for Some Nonlinear Problems with Boundary Value Conditions

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Dionicio Pastor Dallos Santos
Keyword(s):  
Fixed Point ◽  
Continuous Function ◽  
Fixed Point Theorem ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Nonlinear Boundary ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Nonlinear Problems ◽  
Nonlinear Boundary Value Problems

We study the existence of solutions for nonlinear boundary value problemsφu′′=ft,u,u′,  lu,u′=0, wherel(u,u′)=0denotes the boundary conditions on a compact interval0,T,φis a homeomorphism such thatφ(0)=0, andf:0,T×R×R→Ris a continuous function. All the contemplated boundary value problems are reduced to finding a fixed point for one operator defined on a space of functions, and Schauder fixed point theorem or Leray-Schauder degree is used.

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