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

研究拟线性椭圆系统(?)的非平凡非负解或正解的多重性,这里Ω(?)R~N是具有光滑边界(?)Ω的有界域,1≤qp~*/p~*-q,其中当N≤p时,p~*=+∞,而当1

Multiple Results for Quasilinear Elliptic Systems Involving Concave-Convex Nonlinearities and Sign-Changing Weight Functions

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