scholarly journals T-splines and Bézier extraction in modeling shape of boundary in Parametric Integral Equation System for 3D problems of linear elasticity

2019 ◽  
Keyword(s):  
Integral Equation ◽  
Linear Elasticity ◽  
Equation System ◽  
Bézier Extraction

scholarly journals On the Wolff-type Integral System with Negative Exponents

2021 ◽  
Author(s):  
Rong Zhang ◽  
Ling Li
Keyword(s):  
Integral Equation ◽  
Positive Solutions ◽  
Equation System ◽  
Type Condition ◽  
Radial Solutions ◽  
Entire Solutions ◽  
Integral System ◽  
Type Integral ◽  
Bounded Functions ◽  
Type Potential

In this paper, we are concerned with the positive continuous entire solutions of the Wolff-type integral system \begin{equation*} \left\{ \begin{array}{ll} &u(x) =C_{1}(x)W_{\beta,\gamma} (v^{-q})(x), \\[3mm] &v(x) =C_{2}(x)W_{\beta,\gamma} (u^{-p})(x), \end{array} \right. \end{equation*} where $n\geq1$, $\min\{p,q\}>0$, $\gamma>1$, $\beta>0$ and $\beta\gamma\neq n$. In addition, $C_{i}(x) \ (i=1,2)$ are some double bounded functions. If $\beta\gamma\in (0,n)$, the Serrin-type condition is critical for existence of the positive solutions for some double bounded functions $C_{i}(x)$ $(i=1,2)$. Such an integral equation system is related to the study of the $\gamma$-Laplace system and $k$-Hessian system with negative exponents. Estimated by the integral of the Wolff type potential, we obtain the asymptotic rates and the integrability of positive solutions, and studied whether the radial solutions exist.

scholarly journals Existence and symmetry of positive solutions of an integral equation system

2010 ◽  
Vol 52 (5-6) ◽  
pp. 892-901 ◽  
Author(s):  
Xiaotao Huang ◽  
Dongsheng Li ◽  
Lihe Wang
Keyword(s):  
Integral Equation ◽  
Positive Solutions ◽  
Equation System
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