Nonvariational elliptic systems
Nonvariational elliptic systems
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DOI：
10.3934/dcds.2002.8.289
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发表时间：
2002
影响因子：
1.1
通讯作者：
C. O. Alves;D. G. Figueiredo
中科院分区：
文献类型：
--
作者：
C. O. Alves;D. G. Figueiredo
本文对椭圆型方程组（P）$ \qquad\qquad -\Delta u = f（u，v），-\nabla v = g（u，v）$ in $\Omega$u = v = 0$ on $\partial \Omega$提出了次线性和超线性的新概念，其中$\Omega$是光滑有界区域，$f，g$是连续函数.然后利用拓扑方法证明了这类系统正解的存在性。
In this paper, we present new concepts of sublinearity and superlinearity for elliptic systems of the form (P)$ \qquad\qquad -\Delta u = f(u, v), -\nabla v = g(u, v)$ in $\Omega$ $u = v = 0$ on $\partial \Omega$ where $\Omega$ is a smooth bounded domain and $f, g$ are continuous functions. Then we prove existence of positive solutions for such systems via topological methods.