| Budget Amount *help |
¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2014: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2013: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2012: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2011: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2010: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
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| Outline of Final Research Achievements |
We studied nonlinear Dirac equations on compact spin manifolds arising from geometry and physics via variational method. We obtain the following results: 1) For nonlinear Dirac equations obtained as 0-the order nonlinear perturbations of the Dirac operator, we proved the existence and multiplicity of solutions under assuming that the nonlinear term is subcritical. 2) For the case where the nonlinearity has critical growth, we prove a global compactness and the existence of solutions for the associated variational problem. 3) For the Dirac-geodesics problem (which is the 1-dimensional version of Dirac-harmonic maps), we prove the existence of solutions via infinite dimensional Linking theory. 4) For the spinorial Yamabe problem, we proved the existence of a solution via variational argument.
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