scholarly journals Multiple positive solutions for p -Laplacian equations with integral boundary conditions

2017 ◽  
Vol 453 (1) ◽  
pp. 558-571 ◽  
Author(s):  
You-Yuan Yang ◽  
Qi-Ru Wang
Keyword(s):  
Boundary Conditions ◽  
Positive Solutions ◽  
Integral Boundary Conditions ◽  
Multiple Positive Solutions ◽  
Integral Boundary ◽  
Laplacian Equations

scholarly journals Positive Solutions for a Nonlinear Higher Order Differential System with Coupled Integral Boundary Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Yaohong Li ◽  
Haiyan Zhang
Keyword(s):  
Boundary Conditions ◽  
Positive Solutions ◽  
Differential System ◽  
Integral Boundary Conditions ◽  
Higher Order ◽  
Multiple Positive Solutions ◽  
Integral Boundary ◽  
Existence Of Positive Solutions ◽  
The Fixed Point Theorem ◽  
Cone Expansion And Compression

We investigate the existence of positive solutions for a nonlinear higher order differential system, where the differential system is coupled not only in the differential system but also through the boundary conditions. By constructing a special cone and using the fixed point theorem of cone expansion and compression of norm type, the existence of single and multiple positive solutions is established. As an application, we give some examples to demonstrate our results.

scholarly journals Multiple Positive Solutions for a Class of Boundary Value Problem of Fractional p , q -Difference Equations under p , q -Integral Boundary Conditions

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Yongyang Liu ◽  
Yansheng Liu
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Positive Solutions ◽  
Difference Equations ◽  
Topological Degree ◽  
Degree Theory ◽  
Integral Boundary Conditions ◽  
Multiple Positive Solutions ◽  
Topological Degree Theory ◽  
Integral Boundary

This paper is mainly concerned with a class of fractional p , q -difference equations under p , q -integral boundary conditions. Multiple positive solutions are established by using the topological degree theory and Krein–Rutman theorem. Finally, two examples are worked out to illustrate the main results.

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