【摘要】 在局部有限图G=(V,E)上考虑方程组■解的存在性,其中a(x),b(x):V→R,F_u,F_v:V×R~2→R.运用山路引理,证明了方程组在满足(AR)条件或不满足(AR)条件但满足某些其他条件时严格正解的存在性.更多还原

【Abstract】 It was considered the existence of solutions for the following equations ■on locally finite graphs G=(V,E), where a(x), b(x):V→R, F_u, F_v: V×R~2→R. When system satisfied(AR), it was proved that the system had a positive solution by Mountain-Pass Theorem. When the system did not satisfy(AR), it was proved that the system also had a positive solution by Mountain-Pass Theorem under other certain conditions.更多还原