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.
Pomponio, A., Secchi, S. (2004). On a class of singularly perturbed elliptic equations in divergence form: Existence and multiplicity results. JOURNAL OF DIFFERENTIAL EQUATIONS, 207(2), 229-266 [10.1016/j.jde.2004.06.015].
On a class of singularly perturbed elliptic equations in divergence form: Existence and multiplicity results
SECCHI, SIMONE
2004
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))1/2.
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