一类具有组合非线性项的四阶椭圆方程的多重解

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一类具有组合非线性项的四阶椭圆方程的多重解裴瑞昌¹, 张吉慧²1. 天水师范学院数学与统计学院, 天水 741001;
2. 南京师范大学数学科学学院, 南京 210097 Multiple Solutions for a Fourth-order Nonlinear Elliptic Problem with Combined Nonlinearities PEI Ruichang¹, ZHANG Jihui²1. School of Mathematics and Statistics, Tianshui Normal University, Tianshui 741001, China;
2. School of Mathematical Sciences, Nanjing Normal University, Nanjing 210097, China

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摘要利用极小极大方法、Ekeland变分原理和Morse理论建立了一类具有组合非线性项的四阶椭圆方程的五个非平凡解的存在性结果.

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收稿日期: 2013-01-03

PACS:

O175.25

基金资助:国家自然科学基金（11661070）资助项目.

引用本文:

裴瑞昌, 张吉慧. 一类具有组合非线性项的四阶椭圆方程的多重解[J]. 应用数学学报, 2019, 42(2): 167-178. PEI Ruichang, ZHANG Jihui. Multiple Solutions for a Fourth-order Nonlinear Elliptic Problem with Combined Nonlinearities. Acta Mathematicae Applicatae Sinica, 2019, 42(2): 167-178.

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[1]	Ambrosetti, A, Rabinowitz, P H. Dual variational methods in critical point theory and applications. J. Funct. Anal. 14:349-381(1973)
[2]	Brezis, H, Nirenberg, L. Positive solutions of nonlinear elliptic equation involving critical Sobolev exponents. Comm. Pure Appl. Math., 36:437-477(1983)
[3]	Rabinowitz, P H. Minimax Methods in Critical Point Theory with Applications to Differential Equations. CBMs Regional Conference Series in Math., No. 65, American Mathematical Society, Providence, RI, 1986
[4]	Bernis, F, Azorero, J G, Peral, I. Existence and multiplicity of nontrivial solutions in semilinear critical problems of fourth order. Adv. Diff. Equ., 1:219-240(1996)
[5]	Deng, Y B, Wang, G S. On inhomogeneous biharmonic equations involving critical exponents. Proc. Royal Soc. Edinburg, 129:925-946(1999)
[6]	Gazzola, F, Grunau, H C, Squassina, M. Existence and nonexistence results for critical growth biharmonic elliptic equations. Calc. Var. PDE, 18:117-143(2003)
[7]	Noussair, E S, Swanson, C A, Yang, J F. Critical semilinear biharmonic equations in RN. Proc. Royal Soc. Edinburg, 121:139-148(1992)
[8]	Zhou, H S. Existence of asymptotically linear Dirichlet problem. Nonlinear Anal. TMA, 44:909-918(2001)
[9]	Stuart, C A, Zhou, H S. Applying the mountain pass theorem to asymptotically linear elliptic equation on RN. Comm. Part. Diff. Equ., 24:1731-1758(1999)
[10]	Li, G B, Zhou, H S. Multiple solutions to p-Laplacian problems with asymptotic nonlinearity as up-1 at infinity. J. London Math. Soc., 65(2):123-138(2002)
[11]	Ziemer, W P. Weakly Differentiable Functions. Grad. Texts in Math., Vol. 120, Springer-Verlag, Berlin, 1989
[12]	Liu, Y, Wang, Z P. Biharmonic equations with asymptotically linear nonlinearities. Acta Math. Sci., 27:549-560(2007)
[13]	Pei, R C. Multiple solutions for biharmonic equations with asymptotically linear nonlinearities. Boundary value problems, Vol.2010, Article ID 241518, 11, 2010
[14]	Lazer, A C, Mckenna, P J. Large amplitude periodic oscillation in suspension bridges:some new connections with nonlinear analysis. SIAM Rev., 32:537-578(1990)
[15]	Micheletti, A M, Pistoia, A. Multiplicity solutions for a fourth order semilinear elliptic problems. Nonlinear Anal. TMA, 31:895-908(1998)
[16]	Chipot, M. Variational Inequalities and Flow in Porous Media. Springer-Verlag, New York, 1984
[17]	Zhang, J H, Li, S J. Multiple nontrivial solutions for some fourth-order semilinear elliptic problems. Nonlinear Anal. TMA, 60:221-230(2005)
[18]	Chang, K C. Infinite Dimensional Morse Theory and Multiple Solutions Problems. Birkh"auser, Boston, 1993
[19]	Bartsch, T, Li, S J. Critical point theory for asymptotically quadratic functionals and applications to problems with resonance. Nonlinear Anal. TMA, 28:419-441(1997)
[20]	Li, S J, Wu, S P, Zhou, H S. Solutions to semilinear elliptic problems with combined nonlinearities. Journal of Differential Equations, 485:200-224(2002)
[21]	Perera, P. Multiplicity results for some elliptic problems with concave nonlinearities. Journal of Differential Equations, 140:133-141(1997)
[22]	Jiu, Q S, Su, J B. Existence and multiplicity results for Dirichlet problem with p-Laplacian. J. Math. Anal. Appl., 281:587-601(2003)

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