This paper is concerned with the multiplicity of solutions for the nonlinear Dirac equations: View the MathML source−i∑k=13αk∂ku+(V(x)+a)βu+ωu=Fu(x,u). Turn MathJax on Without symmetry assumption on FF, we establish the existence of infinitely many geomet

Using variational analysis, we study the vector optimization problems with objectives being closed multifunctions on Banach spaces or in Asplund spaces. In terms of the coderivatives and normal cones, we present Fermat’s rules as necessary or sufficient conditions for a super efficient solution of the above problems.