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New existence results on nonhomogeneous Sturm-Liouville type BVPs for higher-order p-Laplacian differential equations

100%
Liu Y.
Applicationes Mathematicae
|
2011
|
tom 38
|
nr 3
295-314
EN
A class of nonlinear boundary value problems for p-Laplacian differential equations is studied. Sufficient conditions for the existence of solutions are established. The nonlinearities are allowed to be superlinear. We do not apply the Green's functions of the relevant problem and the methods of obtaining a priori bounds for solutions are different from known ones. Examples that cannot be covered by known results are given to illustrate our theorems.
2
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Studies on BVPs for IFDEs involved with the Riemann-Liouville type fractional derivatives

100%
Liu Y.
Nonautonomous Dynamical Systems
|
2016
|
tom 3
|
nr 1
42-84
EN
In this article, we present a new method for converting the boundary value problems for impulsive fractional differential systems involved with the Riemann-Liouville type derivatives to integral systems, some existence results for solutions of a class of boundary value problems for nonlinear impulsive fractional differential systems at resonance case and non-resonance case are established respectively. Our analysis relies on the well known Schauder’s fixed point theorem and coincidence degree theory. Examples are given to illustrate main results. This paper is motivated by [Solvability of multi-point boundary value problem of nonlinear impulsive fractional differential equation at resonance, Electron. J. Qual. Theory Differ. Equ. 89(2011), 1-19], [Existence result for boundary value problem of nonlinear impulsive fractional differential equation at resonance, J, Appl, Math, Comput. 39(2012) 421-443] and [Solvability for a coupled system of fractional differential equations with impulses at resonance, Bound. Value Probl. 2013, 2013: 80].
3
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IVPs for singular multi-term fractional differential equations with multiple base points and applications

63%
Liu Y., Yang P.
Applicationes Mathematicae
|
2014
|
tom 41
|
nr 4
361-384
EN
The purpose of this paper is to study global existence and uniqueness of solutions of initial value problems for nonlinear fractional differential equations. By constructing a special Banach space and employing fixed-point theorems, some sufficient conditions are obtained for the global existence and uniqueness of solutions of this kind of equations involving Caputo fractional derivatives and multiple base points. We apply the results to solve the forced logistic model with multi-term fractional derivatives.
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