On $p$-Dirac Equation on Compact Spin Manifolds

TL;DR

This paper proves the existence and multiplicity of solutions for p-Dirac equations on compact spin manifolds using variational methods and critical point theory.

Contribution

It introduces new existence and multiplicity results for p-Dirac equations on compact spin manifolds, employing Ljusternik-Schnirelman and biorthogonal system techniques.

Findings

Established a sequence of nonnegative eigenvalues for the p-Dirac operator.

Proved existence of solutions for p-superlinear and p-sublinear nonlinear p-Dirac equations.

Demonstrated multiplicity of solutions 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.