scholarly journals Existence, non-existence and multiplicity results for a third order eigenvalue three-point boundary value problem

2017 ◽  
Vol 10 (10) ◽  
pp. 5445-5463 ◽  
Author(s):  
Alberto Cabada ◽  
Lucía López-Somoza ◽  
Feliz Minhós
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Point Boundary ◽  
Third Order ◽  
Multiplicity Results ◽  
Existence And Multiplicity

scholarly journals Existence and Multiplicity of Solutions for Discrete Nonlinear Two-Point Boundary Value Problems

2011 ◽  
Vol 2011 ◽  
pp. 1-15
Author(s):  
Jianmin Guo ◽  
Caixia Guo
Keyword(s):  
Positive Integer ◽  
Boundary Value Problem ◽  
Critical Point Theory ◽  
Difference Operator ◽  
Boundary Value ◽  
Point Theory ◽  
Point Boundary ◽  
Multiplicity Results ◽  
Existence And Multiplicity ◽  
Forward Difference

By using Morse theory, the critical point theory, and the character of , we consider the existence and multiplicity results of solutions to the following discrete nonlinear two-point boundary value problem subject to , where is a positive integer, is the forward difference operator defined by , and is continuous. In argument, Morse inequalities play an important role.

scholarly journals Positive Solutions for a Class of Third-Order Three-Point Boundary Value Problem

2012 ◽  
Vol 2012 ◽  
pp. 1-12
Author(s):  
Xiaojie Lin ◽  
Zhengmin Fu
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Fixed Point Index ◽  
Boundary Value ◽  
Positive Parameter ◽  
Point Boundary ◽  
Point Index ◽  
Third Order ◽  
Index Theorems ◽  
Existence Of Positive Solutions

We investigate the problem of existence of positive solutions for the nonlinear third-order three-point boundary value problemu‴(t)+λa(t)f(u(t))=0,0<t<1,u(0)=u′(0)=0,u″(1)=∝u″(η), whereλis a positive parameter,∝∈(0,1),η∈(0,1),f:(0,∞)→(0,∞),a:(0,1)→(0,∞)are continuous. Using a specially constructed cone, the fixed point index theorems and Leray-Schauder degree, this work shows the existence and multiplicities of positive solutions for the nonlinear third-order boundary value problem. Some examples are given to demonstrate the main results.

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