EXISTENCE OF SOLUTIONS AND POSITIVITY OF THE INFIMUM EIGENVALUE FOR DEGENERATE ELLIPTIC EQUATIONS WITH VARIABLE EXPONENTS

机译：可变指数的退化椭圆方程的最终椭圆方程的溶液与阳性的存在性

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We study the following nonlinear problem -div(w(x)|▽u|~(p(x)-2)▽u) = λ f(x,u) in Ω which is subject to Dirichlet boundary condition. Under suitable conditions on w and f, employing the variational methods, we show the existence of solutions for the above problem in the weighted variable exponent Lebesgue-Sobolev spaces. Also we obtain the positivity of the infimum eigenvalue for the problem.

机译：我们研究了以下非线性问题-div（w（x）|▽U|▽U|〜（p（x）-2）▽u）=λf（x，u），其ωf（x，u）受到Dirichlet边界条件的影响。在W和F的合适条件下，采用变分方法，我们展示了在加权可变指数Lebesgue-SoboLev空间中的上述问题的解决方案存在。我们也获得了问题的最少特征值的积极性。

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《AIMS International Conference on Dynamical Systems, Differential Equations and Applications》|2013年||共13页
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Inbo Sim; Yun-Ho Kim;
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中图分类微分动力系统;
关键词
p(x)-Laplacian; weighted variable exponent Lebesgue-Sobolev spaces; mountain pass theorem; fountain theorem; eigenvalue.;

机译：p（x）-laplacian;加权变量指数Lebesgue-sobolev spaces;山景定理;喷泉定理;特征值。;

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1. Mountain pass type solutions and positivity of the infimum eigenvalue for quasilinear elliptic equations with variable exponents [J] . Kim In Hyoun, Kim Yun-Ho Manuscripta mathematica . 2015,第1a2期

机译：变指数拟线性椭圆型方程的Mountain Pass型解和最小特征值的正性。
2. Existence and some properties of solutions for degenerate elliptic equations with exponent variable (vol 98, pg 146, 2014) [J] . Ho Ky, Sim Inbo Nonlinear Analysis: An International Multidisciplinary Journal . 2015,第Null期

机译：具有指数变量的退化椭圆型方程解的存在性和某些性质（vol 98，pg 146，2014）
3. Existence and some properties of solutions for degenerate elliptic equations with exponent variable [J] . Ky Ho, Inbo Sim Nonlinear Analysis: An International Multidisciplinary Journal . 2014,第Null期

机译：具有指数变量的退化椭圆型方程解的存在性和一些性质。
4. EXISTENCE OF SOLUTIONS AND POSITIVITY OF THE INFIMUM EIGENVALUE FOR DEGENERATE ELLIPTIC EQUATIONS WITH VARIABLE EXPONENTS [C] . Inbo Sim, Yun-Ho Kim AIMS International Conference on Dynamical Systems, Differential Equations and Applications . 2013

机译：可变指数的退化椭圆方程的最终椭圆方程的溶液与阳性的存在性
5. Existence and bifurcation of multiple positive solutions for some semilinear elliptic equations. [D] . Zhao, Xuejin. 1998

机译：一类半线性椭圆型方程的多个正解的存在性和分歧。
6. On Positive Radial Solutions for a Class of Elliptic Equations [O] . Ying Wu, Guodong Han -1

机译：一类椭圆方程的正径向解
7. Existence of solutions for a fourth order eigenvalue problem ] {Existence of solutions for a fourth order eigenvalue problem with variable exponent under Neumann boundary conditions [O] . Khalil Ben Haddouch, Zakaria El Allali, Najib Tsouli, 2016

机译：四阶特征值问题解的存在性] {Neumann边界条件下具有变指数的四阶特征值问题解的存在性]
8. Existence and Uniqueness Viscosity Solutions of Degenerate Quasilinear Elliptic Equations in R(N). Revision [R] . Crandall, M. G., Newcomb, R., Yoshihito, T. 1988

机译：R（N）中退化拟线性椭圆型方程的存在唯一性粘性解。调整

EXISTENCE OF SOLUTIONS AND POSITIVITY OF THE INFIMUM EIGENVALUE FOR DEGENERATE ELLIPTIC EQUATIONS WITH VARIABLE EXPONENTS

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