743 research outputs found
Nonlinear elliptic Dirichlet problems in exterior domains: the role of geometry and topology of the domain
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Positive solutions of nonlinear elliptic problemsapproximating degenerate equations
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The effect of concentrating potentials in some singularly perturbed problems
No full textThe 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
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