Nodal solutions for some singularly perturbed Dirichlet problems
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- by Teresa D’Aprile and Angela Pistoia PDF
- Trans. Amer. Math. Soc. 363 (2011), 3601-3620 Request permission
Abstract:
We consider the equation $-\varepsilon ^2 \Delta u+u=f(u)$ in a bounded, smooth domain $\Omega \subset \Bbb R^N$ with homogeneous Dirichlet boundary conditions. We prove the existence of nodal solutions with multiple peaks concentrating at different points of $\Omega$. The nonlinearity $f$ grows superlinearly and subcritically. We do not require symmetry conditions on the geometry of the domain.References
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Additional Information
- Teresa D’Aprile
- Affiliation: Dipartimento di Matematica, Università di Roma “Tor Vergata”, via della Ricerca Scientifica 1, 00133 Roma, Italy
- Email: daprile@mat.uniroma2.it
- Angela Pistoia
- Affiliation: Dipartimento di Metodi e Modelli Matematici, Università di Roma “La Sapienza”, via Antonio Scarpa 16, 00161 Roma, Italy
- Email: pistoia@dmmm.uniroma1.it
- Received by editor(s): December 16, 2008
- Received by editor(s) in revised form: October 1, 2009
- Published electronically: February 1, 2011
- Additional Notes: The authors were supported by Mi.U.R. project “Metodi variazionali e topologici nello studio di fenomeni non lineari”.
- © Copyright 2011 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 363 (2011), 3601-3620
- MSC (2010): Primary 35B40, 35J20, 35J57
- DOI: https://doi.org/10.1090/S0002-9947-2011-05221-9
- MathSciNet review: 2775820