scholarly journals More on the explicit solutions for a second-order nonlinear boundary value problem

2008 ◽  
Vol 21 (11) ◽  
pp. 1204-1208 ◽  
Author(s):  
Adil Mısır ◽  
Aydın Tiryaki
Keyword(s):  
Boundary Value Problem ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Second Order ◽  
Nonlinear Boundary Value Problem ◽  
Explicit Solutions ◽  
Nonlinear Boundary Value

The exact number of solutions for the second order nonlinear boundary value problem

2008 ◽  
Vol 58 (4) ◽  
Author(s):  
Peter Somora
Keyword(s):  
Boundary Value Problem ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Second Order ◽  
Nonlinear Boundary Value Problem ◽  
Infinitely Many Solutions ◽  
Number Of Solutions ◽  
Root Functions ◽  
Exact Number ◽  
Nonlinear Boundary Value

AbstractA second order nonlinear differential equation with homogeneous Dirichlet boundary conditions is considered. An explicit expression for the root functions for an autonomous nonlinear boundary value problem is obtained using the results of the paper [SOMORA, P.: The lower bound of the number of solutions for the second order nonlinear boundary value problem via the root functions method, Math. Slovaca 57 (2007), 141–156]. Other assumptions are supposed to prove the monotonicity of root functions and to get the exact number of solutions. The existence of infinitely many solutions of the boundary value problem with strong nonlinearity is obtained by the root function method as well.

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