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On the critical Neumann problem with lower order perturbations

Jan ChabrowskiBernhard Ruf — 2007

Colloquium Mathematicae

We investigate the solvability of the Neumann problem (1.1) involving a critical Sobolev exponent and lower order perturbations in bounded domains. Solutions are obtained by min max methods based on a topological linking. A nonlinear perturbation of a lower order is allowed to interfere with the spectrum of the operator -Δ with the Neumann boundary conditions.

Singularly perturbed elliptic equations with solutions concentrating on a 1-dimensional orbit

Bernhard RufP.N. Srikanth — 2010

Journal of the European Mathematical Society

We consider a singularly perturbed elliptic equation with superlinear nonlinearity on an annulus in 4 , and look for solutions which are invariant under a fixed point free 1-parameter group action. We show that this problem can be reduced to a nonhomogeneous equation on a related annulus in dimension 3. The ground state solutions of this equation are single peak solutions which concentrate near the inner boundary. Transforming back, these solutions produce a family of solutions which concentrate...

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