Existence and boundary behavior of positive solutions for a Sturm-Liouville problem

Masmoudi, S.; Zermani, Samia

doi:10.7494/opmath.2016.36.5.613

Cited by 2 publications

(1 citation statement)

References 23 publications

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“…where is a positive, differentiable function on (0, 1) and satisfying several suitable conditions have been studied by many researchers (see for instance [1][2][3][4][5][6][7][8][9][10]). Note that many problems in the boundary layer theory and the theory of pseudoplastic fluids can be modeled by equations of the form (1) (see for example [11,12]).…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Existence and Global Asymptotic Behavior of Singular Positive Solutions for Radial Laplacian

Bachar

Mâagli

Mesloub

2019

Journal of Function Spaces

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The aim of this paper is to establish existence and uniqueness of a positive continuous solution to the following singular nonlinear problem. {-t1-ntn-1u′′=a(t)uσ, t∈(0,1), limt→0⁡tn-1u′(t)=0, u(1)=0}, where n≥3,σ<1, and a denotes a nonnegative continuous function that might have the property of being singular at t=0 and /or t=1 and which satisfies certain condition associated to Karamata class. We emphasize that the nonlinearity might also be singular at u=0, while the solution could blow-up at 0. Our method is based on the global estimates of potential functions and the Schauder fixed point theorem.

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Section: Introduction and Main Resultsmentioning

confidence: 99%

Existence and Global Asymptotic Behavior of Singular Positive Solutions for Radial Laplacian

Bachar

Mâagli

Mesloub

2019

Journal of Function Spaces

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Fixed point theorems for a class of nonlinear sum-type operators and application in a fractional differential equation

2018

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In this paper, we consider the fixed point for a class of nonlinear sum-type operators 'A + B + C' on an ordered Banach space, where A, B are two mixed monotone operators, C is an increasing operator. Without assuming the existence of upper-lower solutions or compactness or continuity conditions, we prove the unique existence of a positive fixed point and also construct two iterative schemes to approximate it. As applications, we research a nonlinear fractional differential equation with multi-point fractional boundary conditions. By using the obtained fixed point theorems of sum-type operator, we get the sufficient conditions which guarantee the existence and uniqueness of positive solutions. At last, a specific example is provided to illustrate our result. MSC: 47H10; 47H07; 34B10; 34B18

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Existence and boundary behavior of positive solutions for a Sturm-Liouville problem

Cited by 2 publications

References 23 publications

Existence and Global Asymptotic Behavior of Singular Positive Solutions for Radial Laplacian

Existence and Global Asymptotic Behavior of Singular Positive Solutions for Radial Laplacian

Fixed point theorems for a class of nonlinear sum-type operators and application in a fractional differential equation

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