Solutions of nonlinear Dirac equations
Solutions of nonlinear Dirac equations
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DOI：
10.1016/j.jde.2005.08.014
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发表时间：
2006-07-01
影响因子：
2.4
通讯作者：
Ding, Yanheng
中科院分区：
文献类型：
--
作者：
Bartsch, Thomas;Ding, Yanheng
研究了Dirac方程：-i delta（t）psi = ich（3）Sigma（k=1）alpha（k）delta（k）psi - mc（2）beta psi + del（psi）G（x，psi），得到了几类非线性项G：R-3xC-4 -> R模型各种相互作用的定态解的存在性和多解性结果.一个典型的结果表明，如果G（x，u）周期依赖于x，并且在u中是偶数，则该问题有无穷多个几何上不同的局部解。论据是多变的。相应的拉格朗日泛函是强不定的，Palais-Smale条件不成立。我们应用一些最近发展的临界点定理。(c)2005年爱思唯尔公司All rights reserved.
We study the Dirac equation:-i delta(t)psi = ich (3)Sigma(k=1) alpha(k)delta(k)psi - mc(2)beta psi + del(psi)G(x, psi)and obtain existence and multiplicity results of stationary solutions for several classes of nonlinearities G : R-3 x C-4 -> R modeling various types of interaction. A typical result states that if G (x, u) depends periodically on x and is even in u, the problem has infinitely many geometrically different localized solutions. The arguments are variational. The associated Lagrangian functional is strongly indefinite and the Palais-Smale condition does not hold. We apply some recently developed critical point theorems. (c) 2005 Elsevier Inc. All rights reserved.