Existence of three solutions for impulsive multi-point boundary value problems

Böhner, Martin; Heidarkhani, Shapour; Salari, Amjad; Caristi, Giuseppe

doi:10.7494/opmath.2017.37.3.353

Cited by 8 publications

(5 citation statements)

References 37 publications

(30 reference statements)

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“…The main tools are critical points theorems established in [9,10,12]. Variants of such theorems have been successfully applied for other problems, see, e.g., [1,7,8].…”

Section: Introductionmentioning

confidence: 99%

Existence and Multiplicity of Weak Solutions for a Neumann Elliptic Problem with -Laplacian

Böhner

Caristi

Gharehgazlouei

et al. 2020

Nonautonomous Dynamical Systems

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We are interested in the existence of multiple weak solutions for the Neumann elliptic problem involving the anisotropic \vec p-Laplacian operator, on a bounded domain with smooth boundary. We work on the anisotropic variable exponent Sobolev space, and by using a consequence of the local minimum theorem due to Bonanno, we establish existence of at least one weak solution under algebraic conditions on the nonlinear term. Also, we discuss existence of at least two weak solutions for the problem, under algebraic conditions including the classical Ambrosetti–Rabinowitz condition on the nonlinear term. Furthermore, by employing a three critical point theorem due to Bonanno and Marano, we guarantee the existence of at least three weak solutions for the problem in a special case.

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“…The main tools are critical points theorems established in [9,10,12]. Variants of such theorems have been successfully applied for other problems, see, e.g., [1,7,8].…”

Section: Introductionmentioning

confidence: 99%

Existence and Multiplicity of Weak Solutions for a Neumann Elliptic Problem with -Laplacian

Böhner

Caristi

Gharehgazlouei

et al. 2020

Nonautonomous Dynamical Systems

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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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“…Impulsive boundary value problems corresponding to integer-order differential equations with impulsive conditions have been considered extensively in the literature; see [1][2][3] and references therein. Also, in the case of noninteger-order differential equations, there are many results on impulsive boundary value problems; see, for example, [4][5][6][7][8] where t k D α k g k is the Caputo-type fractional differential operator with respect to another increasing differentiable function g k (t), t ∈ J k , of order 1 < α k ≤ 2, J k = (t k , t k+1 ], k = 0, 1, 2, .…”

Section: Introductionmentioning

confidence: 99%

Impulsive boundary value problems containing Caputo fractional derivative of a function with respect to another function

et al. 2019

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In this paper, we study the existence and uniqueness for a new class of impulsive fractional boundary value problems with separated boundary conditions containing the Caputo fractional derivative of a function with respect to another function. The existence of solutions is established by using the Leray-Schauder nonlinear alternative, and the uniqueness result is proved via Banach's contraction mapping principle. Some examples are also constructed to demonstrate the application of main results.

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Existence of three solutions for impulsive multi-point boundary value problems

Cited by 8 publications

References 37 publications

Existence and Multiplicity of Weak Solutions for a Neumann Elliptic Problem with -Laplacian

Existence and Multiplicity of Weak Solutions for a Neumann Elliptic Problem with -Laplacian

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

Impulsive boundary value problems containing Caputo fractional derivative of a function with respect to another function

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