# Nonlinear Equations with Infinitely many Derivatives

@article{Grka2011NonlinearEW, title={Nonlinear Equations with Infinitely many Derivatives}, author={Przemysław G{\'o}rka and Humberto Prado and Enrique G. Reyes}, journal={Complex Analysis and Operator Theory}, year={2011}, volume={5}, pages={313-323} }

- Published 2011
DOI:10.1007/s11785-009-0043-z

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… CONTINUE READING

#### Topics from this paper.

#### Citations

##### Publications citing this paper.

SHOWING 1-7 OF 7 CITATIONS

## A P ] 1 6 Ju l 2 01 8 Nonlinear pseudo-differential equations defined by elliptic symbols on L p ( R n ) and the fractional Laplacian

VIEW 5 EXCERPTS

CITES BACKGROUND & METHODS

HIGHLY INFLUENCED

## Nonlinear pseudo-differential equations defined by elliptic symbols on Lp(ℝn) and the fractional Laplacian

VIEW 5 EXCERPTS

CITES BACKGROUND

HIGHLY INFLUENCED

## Sobolev spaces on locally compact abelian groups

VIEW 2 EXCERPTS

CITES METHODS

## The initial value problem for ordinary differential equations with infinitely many derivatives

VIEW 1 EXCERPT

CITES METHODS

#### Similar Papers

Loading similar papers…