Abstract
A four-point boundary problem for a fractional p-Laplacian differential equation is studied. The existence of two positive solutions is established by means of the monotone iterative method. An example supporting the abstract result is given.
Highlights
Fractional differential equations (FrDEs) are widely used in many fields: physical chemistry, financial mathematics, diffusion theory, transportation theory, chaos and turbulence, viscoelastic mechanics, non-newtonian fluid mechanics, seismic analysis
The standard approach to study boundary value problems (BVPs) for FrDEs is based on the passage to equivalent integral equations and further application of the methods and techniques of modern nonlinear analysis
BVPs involving p-Laplacian have attracted a lot of attention during the last decades
Summary
Fractional differential equations (FrDEs) are widely used in many fields: physical chemistry, financial mathematics, diffusion theory, transportation theory, chaos and turbulence, viscoelastic mechanics, non-newtonian fluid mechanics, seismic analysis. To study (multiple) positive solutions, one can combine the classical Green function methods with fixed point theorems in cones (see, for example, [1,2,3, 5, 7,8,9, 11]). The authors imposed certain monotonicity conditions and applied the upper and lower solutions method.
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