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| Multiplicity of Solutions to Nonlinear Boundary Value Problem with Nonlocal Boundary Condition |
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Citation： |
Zheng Songmu.Multiplicity of Solutions to Nonlinear Boundary Value Problem with Nonlocal Boundary Condition[J].Chinese Annals of Mathematics B,1985,6(1):5~14 |
| Page view： 893
Net amount： 719 |
Authors： |
Zheng Songmu; |
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| Abstract： |
In this paper the author considers the following nonlinear boundary value problem with nonlocal boundary conditions
$[\left\{ \begin{array}{l}
Lu \equiv - \sum\limits_{i,j = 1}^n {\frac{\partial }{{\partial {x_i}}}({a_{ij}}(x)\frac{{\partial u}}{{\partial {x_j}}}) = f(x,u,t)} \u{|_\Gamma } = const, - \int_\Gamma {\sum\limits_{i,j = 1}^n {{a_{ij}}\frac{{\partial u}}{{\partial {x_j}}}\cos (n,{x_i})ds = 0} }
\end{array} \right.\]$
Under suitable assumptions on f it is proved that there exists $t_0\in R,-\infinityt_0, at least one solution at t=t_0 at least two solutions as t |
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