Existence and multiplicity results for some three-point boundary value problems

2007 ◽  
Vol 66 (8) ◽  
pp. 1686-1697 ◽  
Author(s):  
Rahmat Ali Khan ◽  
M. Rafique
Filomat ◽  
2019 ◽  
Vol 33 (3) ◽  
pp. 749-759 ◽  
Author(s):  
Şerife Ege ◽  
Fatma Topal

In this paper, we study the existence and multiplicity of positive solutions to the four-point boundary value problems of nonlinear semipositone fractional differential equations. Our results extend some recent works in the literature.


2004 ◽  
Vol 2004 (11) ◽  
pp. 957-979
Author(s):  
Francesca Dalbono

We prove existence and multiplicity of solutions, with prescribed nodal properties, to a boundary value problem of the formu″+f(t,u)=0,u(0)=u(T)=0. The nonlinearity is supposed to satisfy asymmetric, asymptotically linear assumptions involving indefinite weights. We first study some auxiliary half-linear, two-weighted problems for which an eigenvalue theory holds. Multiplicity is ensured by assumptions expressed in terms of weighted eigenvalues. The proof is developed in the framework of topological methods and is based on some relations between rotation numbers and weighted eigenvalues.


Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 680
Author(s):  
Chan-Gyun Kim

In this paper, we study singular φ -Laplacian nonlocal boundary value problems with a nonlinearity which does not satisfy the L 1 -Carathéodory condition. The existence, nonexistence and/or multiplicity results of positive solutions are established under two different asymptotic behaviors of the nonlinearity at ∞.


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