The equation -epsilon(2) Deltau + a(epsilon)(x)u = f(u) with boundary Dirichlet zero data is considered in a bounded domain Omega subset of R-N. Under the assumption that a(epsilon)(x) greater than or equal to a(infinity) > 0 concentrates, as epsilon --> 0, round a manifold M is an element of Omega and that f is a superlinear function, satisfying suitable growth assumptions, the existence of multiple distinct positive solutions is proved.
The effect of concentrating potentials in some singularly perturbed problems / Cerami, G.; Passaseo, D.. - In: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0944-2669. - STAMPA. - 17:3(2003), pp. 257-281. [10.1007/s00526-002-0169-6]
The effect of concentrating potentials in some singularly perturbed problems
Cerami, G.;
2003-01-01
Abstract
The equation -epsilon(2) Deltau + a(epsilon)(x)u = f(u) with boundary Dirichlet zero data is considered in a bounded domain Omega subset of R-N. Under the assumption that a(epsilon)(x) greater than or equal to a(infinity) > 0 concentrates, as epsilon --> 0, round a manifold M is an element of Omega and that f is a superlinear function, satisfying suitable growth assumptions, the existence of multiple distinct positive solutions is proved.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
