| Abstract: |
| We consider a class of elliptic equations in the whole space $\mathbb R^2$ with weights vanishing at infinity. The decay of the weights that we prescribe enables to study the problem in suitable (limiting) weighted Sobolev space where the maximal growth allowed for the nonlinear term is governed by a weighted version of the Trudinger-Moser inequality. We are concerned with the existence and concentration of solutions in the case of nonlinearities with exponential growth. The results are obtained in collaboration with Joao Marcos do O, Elisandra Gloss and Jianjun Zhang. |
|