Existence of three solutions for impulsive nonlinear fractional boundary value problems

Heidarkhani, Shapour; Феррара, Массимилиано; Caristi, Giuseppe; Salari, Amjad

doi:10.7494/opmath.2017.37.2.281

Cited by 16 publications

(7 citation statements)

References 45 publications

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“…So, by the same process in proof of Theorem 3.1 we have Relations (7) and (8). Since ε is arbitrary, ( 7) and ( 8) gives max 0, lim sup u →+∞ J(u) Φ(u) , lim sup u→(0,...,0) J(u) Φ(u) ≤ 0.…”

Section: Resultsmentioning

confidence: 83%

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Nontrivial solutions for impulsive fractional differential systems through variational methods

Heidarkhani

Salari

2020

Math Methods in App Sciences

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Fractional differential equations (FDEs) as a generalization of ordinary differential equations and integration to arbitrary noninteger orders have gained importance due to their numerous applications in many fields of science and engineering. Indeed, there are a large number of phenomena, including fluid flow, diffusive transport akin to diffusion, rheology, probability, and electrical networks, that are modeled by different equations involving fractional order derivatives. This paper deals with multiplicity results of solutions for a class of impulsive fractional differential systems. The approach is based on variational methods and critical point theory. Indeed, we establish existence results for our system under some algebraic conditions on the nonlinear part with the classical Ambrosetti–Rabinowitz (AR) condition on the nonlinear and the impulsive terms. Moreover by combining two algebraic conditions on the nonlinear term, which guarantee the existence of two weak solutions, applying the mountain pass theorem, we establish the existence of third weak solution for our system.

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Section: Resultsmentioning

confidence: 83%

“…Due to the great development in the theory of fractional calculus and impulsive differential equations as well as having wide applications in several fields. See [2,7,9,17] and the references therein for detailed discussions.…”

Section: Introductionmentioning

confidence: 99%

Nontrivial solutions for impulsive fractional differential systems through variational methods

Heidarkhani

Salari

2020

Math Methods in App Sciences

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“…Let us mention some cases. Bohner et al [3] and Heidarkhani et al [6] presented new criteria on the existence of three solutions for impulsive boundary-value problems. Shang et al [15] and Wang [18] obtained a periodic solution for impulsive differential equations.…”

Section: Introductionmentioning

confidence: 99%

Philos-type oscillation criteria for second-order linear impulsive differential equation with damping

et al. 2019

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In this paper, the problem of oscillation for a second-order linear impulsive differential equation with damping is investigated. This equation can be more accurately used to model the states of many evolutionary processes, which are often subject to short-term perturbations and experience abrupt changes at certain moments of time. By employing a generalized Riccati transformation technique, we derive several oscillation criteria which are either new or improve several recent results in the literature. In addition, we provide an example to illustrate the effect of impulses on the oscillation of the equation.

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“…For example, Heidarkhani et al [26] and [28] studied the following impulsive nonlinear fractional boundary value problem:…”

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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Existence of three solutions for impulsive nonlinear fractional boundary value problems

Cited by 16 publications

References 45 publications

Nontrivial solutions for impulsive fractional differential systems through variational methods

Nontrivial solutions for impulsive fractional differential systems through variational methods

Philos-type oscillation criteria for second-order linear impulsive differential equation with damping

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

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