Positive Steady State Solutions to a Nonlinear Fourth Order Elliptic Equation

机译：非线性四阶椭圆方程的正稳态解

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The paper is devoted to studying a fourth order elliptic equation which has many applications in thin film theory and in the phase transformation theory. By using a truncation function method and a fixed point theorem, the existences of weak solutions and classic solutions for a steady state thin film equation are obtained respectively. Furthermore, the solutions also have positive lower bound. Finally, the viscosity vanishing limit is performed for positive solutions.

机译：本文致力于研究四阶椭圆方程，该方程在薄膜理论和相变理论中都有许多应用。通过使用截断函数法和不动点定理，分别获得了稳态薄膜方程的弱解和经典解的存在性。此外，解决方案还具有正的下限。最后，对正溶液执行粘度消失极限。

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《International conference on cybernetics and informatics》|2014年|2217-2222|共6页
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Bo Liang; Linghua Kong; Fuming Huang;
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Fourth order; Steady state; Higher order;

机译：四阶;稳定状态;高阶;

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1. Jacobi elliptic solutions, solitons and other solutions for the nonlinear Schrodinger equation with fourth-order dispersion and cubic-quintic nonlinearity [J] . Zayed Elsayed M. E., Al-Nowehy Abdul-Ghani European Physical Journal Plus . 2017,第11期

机译：Jacobi椭圆型溶液，孤子和其他具有四阶分散和立方 - QUINTIC非线性的非线性Schrodinger方程的其他解决方案
2. Solutions for fourth-order Kirchhoff type elliptic equations nvolving concave-convex nonlinearities in R~N☆ [J] . Computers & mathematics with applications . 2020,第2期

机译：R〜N中具有凹凸非线性的四阶Kirchhoff型椭圆方程的解☆
3. Multiplicity of Solutions for Fourth-Order Elliptic Equations with p-Laplacian and Mixed Nonlinearity [J] . Mediterranean journal of mathematics . 2020,第2期

机译：具有P-Laplacian和混合非线性的四阶椭圆方程的多种解决方案
4. Positive Steady State Solutions to a Nonlinear Fourth Order Elliptic Equation [C] . Bo Liang, Linghua Kong, Fuming Huang International conference on cybernetics and informatics . 2014

机译：非线性四阶椭圆方程的正稳态解
5. Topics in nonlinear elliptic equations: (1) Bifurcation theory of nonlinear elliptic equations; (2) Spike layer solutions of the Cahn-Hilliard equation. [D] . Shi, Junping. 1998

机译：非线性椭圆方程的主题：（1）非线性椭圆方程的分岔理论；（2）Cahn-Hilliard方程的尖峰层解。
6. Colloquium PaperNonlinear partial differential equations and applications: Some nonlinear elliptic equations from geometry [O] . YanYan Li 2007

机译：非线性偏微分方程及其应用：几何学中的一些非线性椭圆方程
7. Solutions for fourth-order Kirchhoff type elliptic equations involving concave–convex nonlinearities in RN [O] . Dong-Lun Wu, Fengying Li 2020

机译：涉及涉及凹凸非线性的四阶Kirchhoff型椭圆方程的解决方案
8. Positive Eigenfunctions for a Class of Second-Order Elliptic Equations with Strong Nonlinearity. [R] . clement, philippe 1976

机译：一类具有强非线性的二阶椭圆方程的正特征函数。

Positive Steady State Solutions to a Nonlinear Fourth Order Elliptic Equation

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