Singularity theory and the geometry of a nonlinear elliptic equation
On a Superlinear Elliptic Boundary Value Problem.
On the nodal line of the second eigenfunction of elliptic operators in two dimensions.
On the critical Neumann problem with lower order perturbations
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
We consider a singularly perturbed elliptic equation with superlinear nonlinearity on an annulus in , 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...
Multiplicity results for nonlinear elliptic equations
Elliptic equations with one-sided critical growth.
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