Published by Duke University Press since its inception in 1935, the Duke Mathematical Journal is one of the world's leading mathematical journals. Without specializing in a small number of subject areas, it emphasizes the most active and influential areas of current mathematics.

### Volume 69, Number 2

#### Publication Date: February 1993

On the existence of positive solutions of nonlinear elliptic equations—a probabilistic potential theory approach

Z. Zhao; 247-258

$p$-ordinary cohomology groups for $\mathrm{SL}(2)$ over number fields

Haruzo Hida; 259-314

On the standard $L$-function for $G_2$

David Ginzburg; 315-333

Injective analytic maps

András Némethi; 335-347

Variations of the mixed Hodge structure of affine hypersurfaces in algebraic tori

Victor V. Batyrev; 349-409

On the nonvanishing of Rankin-Selberg $\mathrm{L}$-functions

Wenzhi Luo; 411-425

Determination of blow-up solutions with minimal mass for nonlinear Schrödinger equations with critical power

F. Merle; 427-454

Global crystal bases of quantum groups

Masaki Kashiwara; 455-485