A note on the variational structure of an elliptic system involving critical Sobolev exponent. (English) Zbl 1221.35137

Zuluaga, Mario

J. Appl. Math. 2003, No. 5, 227-241 (2003).

Summary: We consider an elliptic system involving critical growth conditions. We develop a technique of variational methods for elliptic systems. Using the well-known results of maximum principle for systems developed by J. Fleckinger et al. [Differ. Integral Equ. 8, No. 1, 69–85 (1995; Zbl 0821.35018)], we can find positive solutions. Also, we generalize the systems results obtained (for the scalar case) by H. Brézis and L. Nirenberg [Commun. Pure Appl. Math. 36, 437–477 (1983; Zbl 0541.35029)]. Also, we give applications to biharmonic equations.

MSC:

35J56	Boundary value problems for first-order elliptic systems
35J50	Variational methods for elliptic systems
35B33	Critical exponents in context of PDEs
35J60	Nonlinear elliptic equations

Citations:

Zbl 0821.35018; Zbl 0541.35029