Solutions for an Euclidean bosonic equation via variational and bifurcation methods.

This paper deals with the study of the existence and multiplicity of solutions for the class of nonlocal problems that have arised in recent developments in the mathematical physics of string theory and cosmology given by (P) { − Δ e − c Δ u + u = λ P (x) (u + f (x , u)) , in R N lim | x | → ∞ ⁡ u (x) = 0 , u ∈ H c , ∞ (R N) , where N ≥ 3 , c > 0 , λ > 0 , P : R N → R is a positive continuous function, f : R N × R → R is C 1 -function, e − c Δ is defined via a power series and H c , ∞ (R N) is a Hilbert space as introduced in [11]. The main tools used here are: the Minimax Theorems and a bifurcation result via variational methods due to Rabinowitz. [ABSTRACT FROM AUTHOR]