On critical exponents curve for nonlinear elliptic equations in zero mass case

Yavdat Il'yasov

Published 2016-05-26Version 1

Semilinear elliptic equations of the form $-\Delta u =\lambda|u|^{p-2}u- |u|^{q-2}u$ in bounded and unbounded domains are considered. In the plane of exponents $p\times q$, the so-called critical exponents curve is introduced which separates domains with qualitatively distinctive properties of the considered equations and the associated parabolic problems. Necessary conditions for solvability to equations, stable and unstable stationary solutions, an existence of global solutions for parabolic problems in the whole space are obtained.