Bonheure, Denis
[UCL]
Van Schaftingen, Jean
[UCL]
In this Note, we deal with stationary nonlinear Schrodinger equations of the form
epsilon(2)Delta u + V(x)u = K(x)u(p), x is an element of R-N,
where V, K > 0 and p > 1 is subcritical. We allow the potential V to vanish at infinity and the competing function K to be unbounded. In this framework, positive ground states may not exist. We prove the existence of at least one positive bound state solution in the semi-classical limit, i.e. for epsilon similar to 0. We also investigate the qualitative properties of the solution as 0.
Bibliographic reference |
Bonheure, Denis ; Van Schaftingen, Jean. Nonlinear Schrodinger equations with potentials vanishing at infinity. In: Comptes rendus - Mathématique, Vol. 342, no. 12, p. 903-908 (2006) |
Permanent URL |
http://hdl.handle.net/2078.1/38398 |