Blow-up phenomena for the Liouville equation with a singular source of integer multiplicity |
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Authors: | Teresa DAprile |
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Institution: | Dipartimento di Matematica, Università di Roma “Tor Vergata”, via della Ricerca Scientifica 1, 00133 Roma, Italy |
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Abstract: | We are concerned with the existence of blowing-up solutions to the following boundary value problem where Ω is a smooth and bounded domain in such that , is a positive smooth function, N is a positive integer and is a small parameter. Here defines the Dirac measure with pole at 0. We find conditions on the function a and on the domain Ω under which there exists a solution blowing up at 0 and satisfying as . |
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Keywords: | 35J20 35J57 35J61 Singular Liouville equation Blowing-up solutions Perturbation methods |
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