By exploiting a variational identity of Pohozaev-Pucci-Serrin type for solutions of class C-1, we get some necessary conditions for locating the peak-points of a class of singularly perturbed quasilinear elliptic problems in divergence form. More precisely, we show that the points where the concentration occurs, in general, must belong to what we call the set of weak-concentration points. Finally, in the semilinear case, we provide a new necessary condition which involves the Clarke subdifferential of the ground-state function
Squassina, M., Secchi, S. (2004). On the location of concentration points for singularly perturbed elliptic equations. ADVANCES IN DIFFERENCE EQUATIONS, 9(1-2), 221-239.
On the location of concentration points for singularly perturbed elliptic equations
Secchi, S
2004
Abstract
By exploiting a variational identity of Pohozaev-Pucci-Serrin type for solutions of class C-1, we get some necessary conditions for locating the peak-points of a class of singularly perturbed quasilinear elliptic problems in divergence form. More precisely, we show that the points where the concentration occurs, in general, must belong to what we call the set of weak-concentration points. Finally, in the semilinear case, we provide a new necessary condition which involves the Clarke subdifferential of the ground-state function
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
