关于零质量情况下nonlinear elliptic方程的临界指数曲线
On critical exponents curve for nonlinear elliptic equations in zero mass case
摘要：
考虑了有界和无界区域上形式为$-Δu =λ|u|^{p-2}u- |u|^{q-2}u$的半线性椭圆型方程。在平面的指数$p\times q$，所谓的临界指数曲线的介绍，它分离域与所考虑的方程和相关的抛物问题的定性独特的属性。得到了方程可解的必要条件，稳定解和不稳定解，抛物型方程在全空间整体解的存在性。
英文摘要：
Semilinear elliptic equations of the form $-Δu =λ|u|^{p-2}u- |u|^{q-2}u$ 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.
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