An Index Theory with Applications to Homoclinic Orbits of Hamiltonian Systems and Dirac Equations
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DOI: 10.1007/s10884-020-09846-3
Abstract: In this paper, we will define the index pair $$(i_A(B),\nu _A(B))$$ ( i A ( B ) , ν A ( B ) ) by the dual variational method, and show the relationship between the… read more here.
Keywords: dirac equations; index; homoclinic orbits; index theory ... See more keywords
Morse–Floer theory for superquadratic Dirac equations, I: relative Morse indices and compactness
Sign Up to like & getrecommendations! Published in 2017 at "Journal of Fixed Point Theory and Applications"
DOI: 10.1007/s11784-016-0391-z
Abstract: In this paper and its sequel (Isobe in Morse–Floer theory for superquadratic Dirac equations, II: construction and computation of Morse–Floer homology, 2016), we study Morse–Floer theory for superquadratic Dirac functionals associated with a class of nonlinear… read more here.
Keywords: dirac equations; morse indices; theory; morse ... See more keywords
Uniqueness of weak solution for Chern–Simons–Dirac equations in R1 + 1
Sign Up to like & getrecommendations! Published in 2017 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2017.03.066
Abstract: Abstract We study the uniqueness of weak solution in L l o c ∞ ( [ 0 , + ∞ ) ; L 2 ( R 1 ) ) for initial value problem of Chern–Simons–Dirac… read more here.
Keywords: dirac equations; chern simons; simons dirac; uniqueness weak ... See more keywords
Einstein-Cartan-Dirac equations in the Newman-Penrose formalism
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DOI: 10.1103/physrevd.98.064046
Abstract: The Dirac equation on a non-torsional space-time has been studied extensively in the Newman-Penrose (NP) formalism. In particular, a comprehensive treatment is given by Chandrasekhar in his book `The Mathematical Theory of Black Holes', which… read more here.
Keywords: dirac equations; einstein cartan; formalism; penrose formalism ... See more keywords
Potential well and multiplicity of solutions for nonlinear Dirac equations
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DOI: 10.3934/cpaa.2020028
Abstract: In this paper we consider the semi-classical solutions of a massive Dirac equations in presence of a critical growth nonlinearity \begin{document}$ -i\hbar \sum\limits_{k = 1}^{3}\alpha_k\partial_k w+a\beta w+V(x)w = f(|w|)w. $\end{document} Under a local condition imposed… read more here.
Keywords: nonlinear dirac; multiplicity solutions; dirac equations; potential well ... See more keywords