Symmetric positive solutions to singular system with multi-point coupled boundary conditions

“…In the aspect of mathematical theory and application, to obtain further information of the relative natural phenomena, many authors are interested in the existence and properties of solutions for fractional differential models [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27] and many analytical techniques and methods have been developed to solve various differential equations, such as iterative methods [28][29][30][31][32][33][34][35][36][37], the Mawhin continuation theorem for resonance [38][39][40], the topological degree method [41,42], the fixed point theorem [43][44][45][46][47][48][49][50][51][52][53][54][55], the variational method [56][57][58]…”

Section: Introductionmentioning

confidence: 99%

Existence and asymptotic analysis of positive solutions for a singular fractional differential equation with nonlocal boundary conditions

Zhang

Liu

et al. 2018

Bound Value Probl

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In this paper, we focus on the existence and asymptotic analysis of positive solutions for a class of singular fractional differential equations subject to nonlocal boundary conditions. By constructing suitable upper and lower solutions and employing Schauder's fixed point theorem, the conditions for the existence of positive solutions are established and the asymptotic analysis for the obtained solution is carried out. In our work, the nonlinear function involved in the equation not only contains fractional derivatives of unknown functions but also has a stronger singularity at some points of the time and space variables.

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“…It is well accepted that fixed point theorems in cones have been instrumental in showing the existence, multiplicity of positive solutions of various boundary value problems for differential equations. See, for instance, [39][40][41][42][43][44][45][46] and the references therein. In this paper, we will use Krasnoselskii's fixed point theorem in a cone to investigate the existence and multiplicity of positive solutions of problem (1.1).…”

Section: Introductionmentioning

confidence: 99%

Multi-parameter second-order impulsive indefinite boundary value problems

Jiao

Zhang

2018

Adv Differ Equ

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We consider the solvable intervals of three positive parameters λ i (i = 1, 2, 3) in which the second-order impulsive boundary value problemx (1) = 0, y(0) = y(1) = 0 admits at least two positive solutions. The main interest is that the weight functions a(t), b(t), and g(t) change sign on [0, 1], λ i (i = 1, 2, 3) ≡ 1, and I k = 0 (k = 1, 2, . . . , n). We will obtain several interesting results: there exist positive constants λ * , λ * , λ * i (i = 1, 3), λ * * i (i = 1, 2, 3) and α with α = 1 such that:and λ 2 ∈ [λ * , λ * ], the above boundary value problem admits at least two positive solutions; (ii) if 0 < α < 1, then for λ i ∈ (0, λ * * i ] (i = 1, 2, 3), the above boundary value problem admits at least two positive solutions.

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Symmetric positive solutions to singular system with multi-point coupled boundary conditions

Cited by 41 publications

References 29 publications

Exact Solutions of the Vakhnenko-Parkes Equation with Complex Method

Exact Solutions of the Vakhnenko-Parkes Equation with Complex Method

Existence and asymptotic analysis of positive solutions for a singular fractional differential equation with nonlocal boundary conditions

Multi-parameter second-order impulsive indefinite boundary value problems

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