一类非线性方程的研究

详细信息

Study on a Generalized Nonlinear Equation

摘要: 在一类推广型非线性方程中,应用Leary-Schauder固定点定律建立了通常Sobolev空间Hs和某个权重Sobolev空间。构建一个方程初值。证明了这类推广型非线性方程的求解问题可简化为求解一个完整性连续图形上固定点φ。应用Leray-Schauder定理来证明图形上所有固定点φ严格在Bx[01]组内部存在,且在Bx[0,1]上的每一点是完全连续。其结果表明,该类推广型方程的解能收敛成初值问题的解,即得到了该类推广型非线性方程唯一光滑解。
- 非线性方程 /
- 光滑解的整体存在性 /
- 初值问题 /
- leary-Schauder固定点定律
Abstract: Using leray-Schauder fixed point theorem with usual sobolev H∞ and certain weighed sobolev spaces build an initial value problem of a class of the extended nonlinear equation. The way of solution this equation can transfer to solution a fixed point φ of integrality uninterrupted figure had been proved. The global existing and uninterrupting of all fixed pointsφ exist in Bx[01] had been proved by using Leray-Schauder fixed point theorem. The result shows that solution of this equation can astringency to solution of initial value problem, get one and only smooth solution of this equation.
- nonlinear equation /
- global existence of smooth solution /
- initial value problem /
- sobolev spaces