We study entire bounded solutions to the equation Δu−u+u3=0 in R2. Our approach is purely variational and is based on concentration arguments and symmetry considerations. This method allows us to construct in an unified way several types of solutions with various symmetries (radial, breather type, rectangular, triangular, hexagonal, etc.), both positive and sign-changing. It is also applicable for more general equations in any dimension.
|Journal||Nonlinear Analysis, Theory, Methods and Applications|
|Early online date||17 Aug 2019|
|Publication status||Published - 1 Jan 2020|
Scopus subject areas
- Applied Mathematics