| 储昌木,唐春雷.具有凹凸非线性项和变号位势函数拟线性椭圆系统解的多重结果[J].数学年刊A辑,2011,32(4):443~458 |
| 具有凹凸非线性项和变号位势函数拟线性椭圆系统解的多重结果 |
| Multiple Results for Quasilinear Elliptic Systems Involving Concave-Convex Nonlinearities and Sign-Changing Weight Functions |
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| DOI： |
| 中文关键词: 拟线性椭圆系统 凹凸非线性项 变号位势函数 Ekeland变分原理 山路引理 |
| 英文关键词:Quasilinear elliptic systems Concave-convex nonlinearities Signchanging weight functions Ekeland's variational principle Mountain pass theorem |
| 基金项目:国家自然科学基金(No11071198)资助的项目 |
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| 中文摘要: |
| $$
-\triangle_pu=\lambda a(x)|u|^{q-2}u+F_u(x,u,v), & x\in\Omega,
-\triangle_p v=\lambda b(x)|v|^{q-2}v+F_v(x,u,v), & x\in\Omega,
u=v=0, & x\in\partial\Omega
$$
的非平凡非负解或正解的多重性, 这里$\Omega \subset \mathbb{R}^{N}$是具有光滑边界$\partial\Omega$的有界域,
$1 \leq q\frac{p^{*}}{p^{*}-q}$,
其中 当$N \leq p$时, $p^{*}=+\infty$, 而当$1 |
| 英文摘要: |
| The multiplicity of nontrivial nonnegative or positive solutions to the following quasilinear elliptic system
$$
-\triangle_pu=\lambda a(x)|u|^{q-2}u+F_u(x,u,v), & x\in\Omega,
-\triangle_pv=\lambda b(x)|v|^{q-2}v+F_v(x,u,v), & x\in\Omega,
u=v=0, & x\in\partial\Omega
$$
is studied, where $\Omega \subset \mathbb{R}^{N}$ is a bounded domain with smooth boundary $\partial\Omega$,
$1\leq q0$ is a positive parameter; $a(x), b(x) \in L^r(\Omega)$ are allowed to change sign,
$r>\frac{p^{*}}{p^{*}-q}$ such that $p^{*}=+\infty$ if $N \leq p$ and $p^{*}=\frac{Np}{N-p}$ if $1 |
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