We study the semiclassical ground states of the Dirac equation with critical nonlinearity in R^3. The Dirac operator is unbounded from below and above, and so the associate energy functional is strongly indefinite. We develop an argument to establish the existence of least energy solutions for small parameters. We also describe the concentration phenomena of the solutions as the parameter goes to zero.
Existence and Concentration of Semiclassical Solutions for Dirac Equations with Critical Nonlinearities / Y. Ding, B. Ruf. - In: SIAM JOURNAL ON MATHEMATICAL ANALYSIS. - ISSN 0036-1410. - 44:6(2012), pp. 3755-3785. [10.1137/110850670]
Existence and Concentration of Semiclassical Solutions for Dirac Equations with Critical Nonlinearities
B. RufUltimo
2012
Abstract
We study the semiclassical ground states of the Dirac equation with critical nonlinearity in R^3. The Dirac operator is unbounded from below and above, and so the associate energy functional is strongly indefinite. We develop an argument to establish the existence of least energy solutions for small parameters. We also describe the concentration phenomena of the solutions as the parameter goes to zero.
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