Mónica Clapp

The effect of the domain topology on the number of minimal nodal solutions of an elliptic equation at critical growth in a symmetric domain

We consider the Dirichlet problem Δu+λu+|u|2*−2u = 0 in Ω, u = 0 on ∂Ω where Ω is a bounded smooth domain in N, N≥4, and 2* = 2N/(N−2) is the critical Sobolev exponent. We show that if Ω is invariant under an orthogonal involution then, for λ>0 sufficiently small, there is an effect of the equivariant topology of Ω on the number of solutions which change sign exactly once.

Intertwining semiclassical bound states to a nonlinear magnetic Schrödinger equation

We consider the magnetic NLS equation where N ? 3, 2 < p < 2* := 2N/(N ? 2), is a magnetic potential and is a bounded electric potential. We consider a group G of orthogonal transformations of , and we assume that A(gx) = gA(x) and V(gx) = V(x) for any g G, . Given a group homomorphism into the unit complex numbers, we show the existence of semiclassical solutions to problem (0.1), which satisfy for all g G, . Moreover, we show that there is a combined effect of the symmetries and the electric potential V on the number of solutions of this type.

Singular limits for the bi-Laplacian operator with exponential nonlinearity in R4

Let

A Global Compactness Result for Elliptic Problems with Critical Nonlinearity on Symmetric Domains

\Omega

Multiple Solutions of Nonlinear Scalar Field Equations

be a bounded smooth domain in

The homotopy category of parametrized spectra

\mathbb{R}^{4}

TWO SOLUTIONS OF THE BAHRI–CORON PROBLEM IN PUNCTURED DOMAINS VIA THE FIXED POINT TRANSFER

such that for some integer

Critical point theory for perturbations of symmetric functionals

d\geq1

Alternating Sign Multibump Solutions of Nonlinear Elliptic Equations in Expanding Tubular Domains

its

Upper estimates for the energy of solutions of nonhomogeneous boundary value problems

d