Infinitely many solutions for perturbed impulsive fractional differential systems

Heidarkhani, Shapour; Zhao, Yulin; Caristi, Giuseppe; Afrouzi, G. A.; Moradi, Shahpoor

doi:10.1080/00036811.2016.1192147

Cited by 26 publications

(13 citation statements)

References 33 publications

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“…We also cite the papers [29,30,31,32,33] in which fractional systems have been studied. In [32,33], through variational methods and critical point theory the existence of multiple solutions for coupled systems of nonlinear fractional differential equations was analyzed.…”

Section: Introductionmentioning

confidence: 99%

Energy estimate for impulsive fractional advection dispersion equations in anomalous diffusions

2018

J. Nonlinear Funct. Anal.

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This paper deals with the existence and energy estimates of solutions for a class of impulsive fractional advection dispersion equations in anomalous diffusions, while the nonlinear part of the problem admits some hypotheses on the behavior at origin or perturbation property. In particular, for a precise localization of the parameter, the existence of a non-zero solution is established requiring the sublinearity of nonlinear part at origin and infinity. We also consider the existence of solutions for our problem under algebraic conditions with the classical Ambrosetti-Rabinowitz. By combining two algebraic conditions on the nonlinear term which guarantees the existence of two solutions as well as applying the mountain pass theorem given by Pucci and Serrin, we establish the existence of the third solution for our problem. Moreover, concrete examples of applications are also provided.

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Section: Introductionmentioning

confidence: 99%

Energy estimate for impulsive fractional advection dispersion equations in anomalous diffusions

2018

J. Nonlinear Funct. Anal.

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“…For details, see [18][19][20][21] and the references therein. Recently, many authors have studied the existence of solutions for impulsive fractional boundary value problem by using variational methods and critical point theory, see [22][23][24][25][26][27][28][29][30].…”

Section: + U(t)) + |U(t)| P-2 U(t) = F (T U(t)) T ∈ [0 T] T = T Jmentioning

confidence: 99%

Infinitely many solutions for impulsive fractional boundary value problem with p-Laplacian

2018

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“…We also refer the reader to [25,26] in which using variational methods and critical point theory the existence of multiple solutions for impulsive fractional differential systems were discussed.…”

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confidence: 99%

Existence of three solutions for impulsive nonlinear fractional boundary value problems

Heidarkhani

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Caristi

et al. 2017

OpMath

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Infinitely many solutions for perturbed impulsive fractional differential systems

Cited by 26 publications

References 33 publications

Energy estimate for impulsive fractional advection dispersion equations in anomalous diffusions

Energy estimate for impulsive fractional advection dispersion equations in anomalous diffusions

Infinitely many solutions for impulsive fractional boundary value problem with p-Laplacian

Existence of three solutions for impulsive nonlinear fractional boundary value problems

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