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| The Existence Theorem for Solutions of General Boundary Value Problemof Quasi-Linear Second Order Elliptic Differential Equations |
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Citation： |
Zhu Rujin.The Existence Theorem for Solutions of General Boundary Value Problemof Quasi-Linear Second Order Elliptic Differential Equations[J].Chinese Annals of Mathematics B,1982,3(2):159~168 |
| Page view： 854
Net amount： 792 |
Authors： |
Zhu Rujin; |
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| Abstract： |
In this paper, we provide the existence theorem for solutions of general boundary value problem of quasi-linear second order elliptic differential equations in the following form:
$\[\sum\limits_{i,j = 1}^n {({a_{ij}}(x,u)\frac{{\partial u}}{{\partial {x_j}}}) + a(x,u,{u_{{x_k}}}),{\rm{ }}in} {\rm{ }}\Omega \]$,
$\[\alpha (x,u)\frac{{\partial u}}{{\partial \gamma }} + \beta (x,u) = 0,{\rm{ on }}\partial \Omega \]$,
where \alpha(x, u) \geq 0,\alpha_u(x, u) \leq 0 and \gamma is some direction, defining on $\[\partial \Omega \]$. |
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