2024/08/29 by Qi, Wanting, Zhang, Xingyong
#Analysis of PDEs (math.AP) #FOS: Mathematics
paper · doi:10.48550/arxiv.2408.16364
We investigate the existence and multiplicity of solutions for a class of generalized coupled system involving poly-Laplacian and a parameter λ on finite graphs. By using mountain pass lemma together with cut-off technique, we obtain that system has at least a nontrivial weak solution (uλ,vλ) for every large parameter λ when the nonlinear term F(x,u,v) satisfies superlinear growth conditions only in a neighborhood of origin point (0,0). We also obtain a concrete form for the lower bound of parameter λ and the trend of (uλ,vλ) with the change of parameter λ. Moreover, by using a revised Clark's theorem together with cut-off technique, we obtain that system has a sequence of solutions tending to 0 for every λ>0 when the nonlinear term F(x,u,v) satisfies sublinear growth conditions only in a neighborhood of origin point (0,0).