一类p(x)-Laplace方程解的存在性研究

Existence of Solution for a Class of Equation

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摘要在光滑有界区域Ω奂RN上,讨论了具有Dirichlet边值条件的一类p(x)-Laplace方程解的存在性.在问题的研究过程中,通过利用LP(x)(Ω)空间,W1,P(x)(Ω)空间的一些相关理论及带有PS条件的Mountain Pass引理,给出了解存在性的一个充分条件,对原有结论进行了一个有意义的推广. In this paper, the existence of solution for a class of p（x）-Laplace equation with Dirichlet boundary value was discussed. An existence result which generalized the work of G. A. Afrouzi independing on the spaces of LP（x）（Ω） ,W1P（x）（Ω） and the Mountain Pass Lemma was obtained.

作者孙健刘辉昭

机构地区天津中德应用技术大学基础课部河北工业大学理学院

出处《广东技术师范学院学报》 2016年第8期1-3,共3页 Journal of Guangdong Polytechnic Normal University

关键词 P(X)-LAPLACE方程 PS条件 MOUNTAIN Pass引理 p（x）-Laplace equation PS condition Mountain Pass Lemma

分类号 O175.2 [理学—基础数学]

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参考文献5

1Xian ling Fan, Qi Hu Zhang. Existence of solutions for p(x) -Laplacian Dirichlet probolem [J]. Nonlinear Analysis, 200 3,52: 1843-1852.
2Fan X L, Shen J, Zhao D. Sobolev Embeding Theorems for spaces [J]. Math Anal Appl, 2001, 262(2):749-760.
3范先令,赵元章,张启虎.p(x)-Laplace方程的强极大值原理[J].数学年刊（A辑）,2003,24(4):495-500. 被引量：6
4Wang X, Zhao L, Zhao P H. Combined effects of singular and critical nonlinearities in elliptic problems[J]. Nonlinear Analysis: Theory, Method & Applications, 2013, 87:1-10.
5G. A . Afrouzi, On positive mountain pass solutions for a semilinear elliptic boundary value problem [J]. Applied Mat hematics and Computation. 2005, 167: 76-80.

二级参考文献13

1Zhikov, V. V., Averaging of functionals of the calculus of variations and elasticity theory[J], Math. USSR. Izv., 29(1987), 33-36.
2Marcellini, P., Regularity and existence of solutions of elliptic equations with p, q-growth conditions [J], J. Diff. Zqu., 90(1991), 1-30.
3Fan, X. L. & Zhao, D., A class of De Giorgi type and HSlder continuity [J], Nonlinear Anal., 36(1999), 295-318.
4Fan, X. L. & Zhao, D., The quasi-minimizer of integral functionals with m(x)-growth conditions [J], Nonlinear Anal., 39:7(2000), 807-816.
5Pratter, M. & Weinberger, H. F., Maximum principles in differential equations [M],Prentice Hall, Englewood Cliffs, N J, 1967.
6Trudinger, N. S., On Harnack type inequahties and their application to quasi-hnear elliptic equations [J], Comm. Pure Appl. Math., 20(1967), 721-747.
7Vazqucz, J. L., A strong maximum principle for some quasilinear elliptic equations [J],Appl. Math. Optim., 12(1984), 191-202.
8Heinonen, J., Kilpelainen, T. & Martio, O., Nonlinear potential theory of degenerate elliptic equations [M], Clarendon Press, Oxford 1993.
9Garcia-Melian, J. & Sabina de Lis, J., Maximum and comparison principles for operators involving the p-Laplacian [J], J. Math. Anal. Appl., 218(1998), 49-65.
10Montenegro, M., Strong maximum principles for super-solutions of quasilinear elliptic equations [J], Nonlinear Anal., 37(1999), 431-448.

共引文献5

1邓志颖,刘祥清.一类含Hardy奇异项的p(x)-Laplace方程的正解[J].湖北民族学院学报（自然科学版）,2011,29(4):361-367.
2柳彦军,张伟,蔡银英.含奇异项与临界项的非线性椭圆方程[J].应用泛函分析学报,2015,17(3):262-269.
3孙健,张学东.关于一类p(x)—Laplacian方程组解的存在性研究[J].廊坊师范学院学报（自然科学版）,2016,16(1):19-22.
4赵凯芳,刘辉昭,丁纺.一类带有梯度的p(x)-Laplace方程正解的存在性[J].河北工业大学学报,2016,45(3):21-27.
5孙健,刘辉昭.一类p(x)-Laplace方程边值问题解的存在性研究[J].郑州师范教育,2016,5(4):5-7.

1Lu Yuefeng Li Chengyue Zhong Shizeng Zhang Weijie.HOMOCLINIC ORBITS FOR A CLASS OF HAMILTONIAN SYSTEMS WITH POTENTIALS CHANGING SIGN[J].Annals of Differential Equations,2005,21(3):370-372. 被引量：1
2孙健.关于p-Laplace方程解的存在性[J].南阳师范学院学报,2016,15(3):12-15.
3孙健,刘辉昭.一类p(x)-Laplace方程边值问题解的存在性研究[J].郑州师范教育,2016,5(4):5-7.
4孙健,张学东.关于一类p(x)—Laplacian方程组解的存在性研究[J].廊坊师范学院学报（自然科学版）,2016,16(1):19-22.
5周焕松.POSITIVE SOLUTIONS FOR A DIRICHLET PROBLEM[J].Acta Mathematicae Applicatae Sinica,2001,17(3):340-349.
6XUAN Benjin,CHEN Zuchi (Department of Mathematics, University of Science and Technology of China, Hefei 230026, China).EXISTENCE, MULTIPLICITY AND BIFURCATION FOR CRITICAL POLYHARMONIC EQUATIONS[J].Systems Science and Mathematical Sciences,1999,12(1):59-69. 被引量：7
7WU Shaoping (Department of Mathematics, Zhejiang University, Hangzhou 310027, China).A HOMOCLINIC ORBIT FOR LAGRANGIAN SYSTEMS[J].Systems Science and Mathematical Sciences,1995,8(1):75-81.
8ZHOU Huan Song Laboratory of Mathematical Physics. Wuhan Institute of Physics and Mathematics. Chinese Academy of Sciences, P. O. Box 71010, Wuhan 430071. P. R. China.An Application of a Mountain Pass Theorem[J].Acta Mathematica Sinica,English Series,2002,18(1):27-36. 被引量：18
9张宪君,戚桂杰.On Theorem of the “Mountain Im passe”Type[J].Chinese Quarterly Journal of Mathematics,1998,13(1):107-110.
10Tang Chunlei, Department of Mathematics, Southwest Normal University, Chongqing 400715, China.Periodic Solutions for Second Order Systems at Resonance[J].Acta Mathematica Sinica,English Series,1998,14(4):433-440. 被引量：4

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一类p(x)-Laplace方程解的存在性研究

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