Bifurcation from infinity and multiple solutions for an elliptic system
Raffaele Chiappinelli, Djairo Guedes De Figueiredo · Differential and Integral Equations · 1993
In this paper, we study multiplicity of solutions for a system of semilinear elliptic equations of the formin some bounded smooth domain in JRN, subject to homogeneous Dirichlet boundary conditions.The parameters 8 and 1' are positive and satisfy certain relations involving also the first eigenvalue Al of {-D.o,H 1 {0)).The parameter A varies in a neighborhood of ).1 := Al + 8 /(1' + Al ).We establish a priori bounds for solutions of the system when A is an appropriate side of).~, depending on the behavior of f(x,s) and s--.±oo.These bounds, together with a bifurcation from infinity, gives the multiplicity results.(u, v) of] solutions under various assumptions on J, using both monotone iteration techniques and variational methods.In this paper, we study existence and multiplicity of solutions to (8>.) when..\ is near >.1,