On $p$-Dirac Equation on Compact Spin Manifolds

Abstract

By using the Ljusternik-Schnirelman principle, we establish the existence of a nondecreasing sequence of nonnegative eigenvalues for the p-Dirac operator on compact spin manifold. Using the biorthogonal system theory on separable Banach space and some critical point theorems, we prove the existence and multiplicity of solutions to p-superlinear and p-sublinear nonlinear p-Dirac equations on compact spin manifold.