scholarly journals On the asymptotic behavior of positive solutions of certain integral equations

2015 ◽  
Vol 44 ◽  
pp. 5-11
Author(s):  
Said R. Grace
Keyword(s):  
Asymptotic Behavior ◽  
Integral Equations ◽  
Positive Solutions

scholarly journals Quantitative analysis of a system of integral equations with weight on the upper half space

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Sufang Tang ◽  
Jingbo Dou
Keyword(s):  
Growth Rate ◽  
Asymptotic Behavior ◽  
Quantitative Analysis ◽  
Decay Rate ◽  
Integral Equations ◽  
Half Space ◽  
Positive Solutions ◽  
Sobolev Inequality ◽  
System Of Integral Equations ◽  
Lagrange System

<p style='text-indent:20px;'>In this paper we analyzed the integrability and asymptotic behavior of the positive solutions to the Euler-Lagrange system associated with a class of weighted Hardy-Littlewood-Sobolev inequality on the upper half space <inline-formula><tex-math id="M1">\begin{document}$ \mathbb{R}_+^n. $\end{document}</tex-math></inline-formula> We first obtained the optimal integrability for the solutions by the regularity lifting theorem. And then, with this integrability, we investigated the growth rate of the solutions around the origin and the decay rate near infinity.</p>

Existence and asymptotical behavior of solutions for a quasilinear Choquard equation with singularity

2021 ◽  
Vol 19 (1) ◽  
pp. 259-267
Author(s):  
Liuyang Shao ◽  
Yingmin Wang
Keyword(s):  
Asymptotic Behavior ◽  
Positive Solutions ◽  
Riesz Potential ◽  
Asymptotic Behavior Of Solutions ◽  
Suitable Assumption ◽  
Choquard Equation ◽  
Existence Of Positive Solutions

Abstract In this study, we consider the following quasilinear Choquard equation with singularity − Δ u + V ( x ) u − u Δ u 2 + λ ( I α ∗ ∣ u ∣ p ) ∣ u ∣ p − 2 u = K ( x ) u − γ , x ∈ R N , u > 0 , x ∈ R N , \left\{\begin{array}{ll}-\Delta u+V\left(x)u-u\Delta {u}^{2}+\lambda \left({I}_{\alpha }\ast | u{| }^{p})| u{| }^{p-2}u=K\left(x){u}^{-\gamma },\hspace{1.0em}& x\in {{\mathbb{R}}}^{N},\\ u\gt 0,\hspace{1.0em}& x\in {{\mathbb{R}}}^{N},\end{array}\right. where I α {I}_{\alpha } is a Riesz potential, 0 < α < N 0\lt \alpha \lt N , and N + α N < p < N + α N − 2 \displaystyle \frac{N+\alpha }{N}\lt p\lt \displaystyle \frac{N+\alpha }{N-2} , with λ > 0 \lambda \gt 0 . Under suitable assumption on V V and K K , we research the existence of positive solutions of the equations. Furthermore, we obtain the asymptotic behavior of solutions as λ → 0 \lambda \to 0 .

scholarly journals Existence and Exact Asymptotic Behavior of Positive Solutions for a Fractional Boundary Value Problem

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Habib Mâagli ◽  
Noureddine Mhadhebi ◽  
Noureddine Zeddini
Keyword(s):  
Asymptotic Behavior ◽  
Continuous Function ◽  
Boundary Value Problem ◽  
Positive Solution ◽  
Positive Solutions ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Fractional Boundary Value Problem ◽  
Exact Asymptotic Behavior ◽  
Nonnegative Continuous Function

We establish the existence and uniqueness of a positive solution for the fractional boundary value problem , with the condition , where , and is a nonnegative continuous function on that may be singular at or .

scholarly journals Asymptotic behavior of fractional order Riemann-Liouville Volterra-Stieltjes integral equations

2015 ◽  
Vol 27 (3) ◽  
pp. 311-323
Author(s):  
Saïd Abbas ◽  
Mouffak Benchohra ◽  
Boualem A. Slimani ◽  
Juan J. Trujillo
Keyword(s):  
Asymptotic Behavior ◽  
Integral Equations ◽  
Fractional Order ◽  
Stieltjes Integral

scholarly journals Asymptotic Behavior of Solutions of Integral Equations with Homogeneous Kernels

Mathematics ◽  
2022 ◽  
Vol 10 (2) ◽  
pp. 180
Author(s):  
Oleg Avsyankin
Keyword(s):  
Integral Equation ◽  
Asymptotic Behavior ◽  
Integral Equations ◽  
Spherical Harmonics ◽  
Special Class ◽  
Continuous Functions ◽  
Asymptotic Behavior Of Solutions ◽  
Free Term ◽  
Research Technique ◽  
Multidimensional Integral

The multidimensional integral equation of second kind with a homogeneous of degree (−n) kernel is considered. The special class of continuous functions with a given asymptotic behavior in the neighborhood of zero is defined. It is proved that, if the free term of the integral equation belongs to this class and the equation itself is solvable, then its solution also belongs to this class. To solve this problem, a special research technique is used. The above-mentioned technique is based on the decomposition of both the solution and the free term in spherical harmonics.

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