Nonlinear Eigenvalue Problems and Bifurcation for Quasi-Linear Elliptic Operators

Abstract In this paper, we analyze an eigenvalue problem for quasi-linear elliptic operators involving homogeneous Dirichlet boundary conditions in a open smooth bounded domain. We show that the eigenfunctions corresponding to eigenvalues belong $$L^{\infty }$$ L ∞ , which implies $$C^{1,\alpha C 1 , α smoothness, and first is simple. Moreover, investigate bifurcation results from trivial solutions using Krasnoselski theorem infinity Leray–Schauder degree. also existence of multiple critical points variational methods genus.