| Abstract: |
| We discuss implications of an energy conservation identity
on properties of solutions for some second order ODE`s with Hamiltonian structure.
Variational proofs of existence of solutions for semilinear elliptic PDE`s are often based on
compactness of embeddings between the appropriate functional spaces.
In the case of critical or super-critical nonlinearities, the loss of compactness is manifested
in the concentration of minimizing sequences at critical points or at singularities of the potential.
This identity is able to capture the loss of compactness for radial functions in some special
cases of rotationally symmetric PDE`s. |
|