×

zbMATH — the first resource for mathematics

Nonzero and positive solutions of a superlinear elliptic system. (English) Zbl 1090.35525
The author considers an undecoupling elliptic system \[ -\Delta u = \lambda u + \delta v + | u | ^{r-1}, \qquad -\Delta v = \theta u + \gamma v + | v | ^{s-1} \] in \(\Omega \subset \mathbb R^n\), \(n\geq 4\), with zero Dirichlet condition. The exponents are assumed to satisfy \(r > 2\), \( s < 2^* = \frac {2n}{n-2}\). Using Leray-Schauder degree theory and measure theory he shows the existence of positive solutions, under conditions relating the spectrum of \(-\Delta \) and the coefficients of the system. Further, applications to biharmonic equations and the scalar case are given.

MSC:
35J55 Systems of elliptic equations, boundary value problems (MSC2000)
47H11 Degree theory for nonlinear operators
PDF BibTeX XML Cite
Full Text: EMIS EuDML