Bounds for the spectrum and the norm of solutions of nonlinear elliptic equations and systems
โ Scribed by C Cosner; M.H Protter
- Publisher
- Elsevier Science
- Year
- 1985
- Tongue
- English
- Weight
- 790 KB
- Volume
- 56
- Category
- Article
- ISSN
- 0022-0396
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๐ SIMILAR VOLUMES
## Abstract We introduce a measure for the starshapedness of the level sets of solutions of certain nonlinear elliptic equations in a starshaped ring ฮฉ of IR^n^. We prove that a function which characterizes the starshapedness does not attain its minimum in ฮฉ.
Let M u, ยจs 0, N u, ยจs 0 define two distinct phase curves โซ , โซ in the 1 2 ลฝ . u,ยจ-phase plane. This paper presents results on the relationships among the positive equilibria, the phase curves, and the existence of positive solutions to the PDE system โฌ u q uM u, ยจs 0, โฌยจq ยจN u, ยจs 0 in โ;R n ลฝ . ลฝ