We study the generalized bosonic string equation $$ \Delta e^{-c\,\Delta}\phi = U(x,\phi), \quad c > 0$$ on Euclidean space $${\mathbb {R}^n}$$ . First, we interpret the nonlocal operator $${\Delta e^{-c\,\Delta}}$$ using entire vectors of Δ in $${L^2(\mathbb{R}^n)}$$ , and we show that if $${U(x, \phi) = \phi(x) + f(x)}$$ , in which $${f \in L^2(\mathbb {R}^n)}$$ , then there exists a unique real-analytic solution to the Euclidean bosonic string in a Hilbert space $${{\mathcal H}^{c,\infty}(\mathbb {R}^n)}$$ we define precisely below. Second, we consider the case in which the potential $${U(x, \phi)}$$ in the generalized bosonic string equation depends nonlinearly on $${\phi}$$ , and we show that this equation admits real-analytic solutions in $${{\mathcal H}^{c,\infty}(\mathbb R^n)}$$ under some symmetry and growth assumptions on U. Finally, we show that the above given equation admits real-analytic solutions in $${{\mathcal H}^{c,\infty}(\mathbb {R}^n)}$$ if $${U(x, \phi)}$$ is suitably near $${U_0(x, \phi) = \phi}$$ , even if no symmetry assumptions are imposed.