scholarly journals New fixed point index results and nonlinear boundary value problems

2017 ◽  
Vol 49 (3) ◽  
pp. 534-547 ◽  
Author(s):  
J. R. L. Webb
Keyword(s):  
Fixed Point ◽  
Boundary Value Problems ◽  
Fixed Point Index ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Point Index ◽  
Nonlinear Boundary Value Problems ◽  
Nonlinear Boundary Value

scholarly journals The Application of Distributional Henstock-Kurzweil Integral on Third-order Three-Point Nonlinear Boundary-Value Problems

2015 ◽  
Vol 7 (4) ◽  
pp. 150
Author(s):  
Dakai Zhou ◽  
Guoju Ye ◽  
Wei Liu ◽  
Bing Liang
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problems ◽  
Point Theorem ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Nonlinear Boundary Value Problems ◽  
Third Order ◽  
Nonlinear Boundary Value

We consider a type of form such as $u'''=-f$ with three-point<br />nonlinear boundary-value problems (NBVPs). We verified the existence<br />of solutions of the (NBVPs) when $f$ is distributional<br />Henstock-Kurzweil integral but not Henstock-Kurzweil integral.We use<br />the distribution derivative and fixed point theorem to deal with the<br />problem. The results obtained generalize the known results. For<br />this reason, it is conducive to the further study of NBVPS.

POSITIVE SOLUTIONS FOR SYSTEMS OF M‐POINT NONLINEAR BOUNDARY VALUE PROBLEMS

2008 ◽  
Vol 13 (3) ◽  
pp. 357-370 ◽  
Author(s):  
Johnny Henderson ◽  
Sotiris K. Ntouyas ◽  
Ioannis K. Purnaras
Keyword(s):  
Fixed Point ◽  
Nonlinear System ◽  
Fixed Point Theorem ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Point Theorem ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Nonlinear Boundary Value Problems ◽  
Nonlinear Boundary Value

Positive solutions (u(t), v(t)) are sought for the nonlocal (m‐point) nonlinear system of boundary value problems, u” + λa(t)f(v) = 0, v” + λb(t)g(u) = 0, for 0 < t < 1, and satisfying, u(0) = 0, u(1) = . An application of a Guo‐Krasnosel'skii fixed point theorem yields sufficient values of λ for which such positive solutions exist.

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