The main purpose of this paper is to study the existence of single-peaked positive solutions of the singularly perturbed elliptic equation -ε2 div (J(x)∇ u) + V(x) u = f(u) in ℝN , where J is a symmetric uniformly elliptic matrix and V is a positive potential, possibly unbounded from above. If f(u) = up , then solutions concentrate at non-degenerate critical points of Γ (x) = V(x)p+1/p-1-N/2 (det J (x))1/2
On a class of singularly perturbed elliptic equations in divergence form: existence and multiplicity results / Pomponio, A.; Secchi, S.. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - STAMPA. - 207:2(2004), pp. 229-266. [10.1016/j.jde.2004.06.015]
On a class of singularly perturbed elliptic equations in divergence form: existence and multiplicity results
Pomponio, A.;
2004-01-01
Abstract
The main purpose of this paper is to study the existence of single-peaked positive solutions of the singularly perturbed elliptic equation -ε2 div (J(x)∇ u) + V(x) u = f(u) in ℝN , where J is a symmetric uniformly elliptic matrix and V is a positive potential, possibly unbounded from above. If f(u) = up , then solutions concentrate at non-degenerate critical points of Γ (x) = V(x)p+1/p-1-N/2 (det J (x))1/2I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
