Four-Parameter Bifurcation for a p-Laplacian system
Jacqueline Fleckinger‐Pellé, Rosa Pardo San Gil, François de Thélin · 2001
We study a four-parameter bifurcation phenomenum arising in a system involvingp-Laplacians: pu=ap(u)+bp(v)+f(a;p(u);p(v)); pv=cp(u)+dp(v))+g(d;p(u);p(v)); with u = v = 0 on the boundary of a bounded and suciently smooth domain in R N ;h ere p u =d iv(jruj p 2 ru), with p> 1a nd p 6 , is the p-Laplacian operator, and p(s )= j s j p 2 swith p> 1. We assume that a;b;c;d are real parameters. Thwn we use a bifurcation method to exhibit some nontrivial solutions. The associated eigenvalue problem, withf =g0, is also studied here.