Spectral bounds for Tricomi problems and application to semilinear existence and existence with uniqueness results
Articolo
Data di Pubblicazione:
2002
Citazione:
Spectral bounds for Tricomi problems and application to semilinear existence and existence with uniqueness results / Daniela Lupo, Kevin R. Payne. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - 184(2002):1(2002), pp. 139-162.
Abstract:
For the linear Tricomi problem it is shown that real eigenvalues corresponding to generalized eigenfunctions must be positive and that the energy integral methods used to prove solvability results can give lower bounds on the spectrum. Exploiting the linear
solvability theory and spectral information standard nonlinear analysis tools are employed to yield results on existence and
uniqueness for semilinear problems. In particular, using the Leray-Schauder principle existence of generalized solutions with sublinear nonlinearities is established. For sublinear or asymptotically linear nonlinearities that satisfy a Lipschitz
condition, the contraction mapping principle is employed to give results on existence with uniqueness. The Lipschitz constant depends on lower bounds for the spectrum of the linear problem. For certain superlinear problems, maximum principles for the linear problem are used via the method of upper and lower solutions to give results on existence.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Spectral theory, maximum principle, Tricomi problem, fixed point theorems, monotone methods
Elenco autori:
Daniela Lupo, Kevin R. Payne
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