论文导读:本文讨论了一类非线性项在负无穷远处为渐近线性,在正无穷远处为超线性的四阶非线性椭圆方程问题,并通过山路引理和实分析的方法获得了该问题在空间中的非平凡弱解存在性的结论.
关键词:四阶椭圆方程渐近线性,超线性山路引理
参考文献
1 A. Ambrosetti, P. Rabinowitz, Dual variationalmethods in critical point theory and applications[J], J Funct Anal, 1973,14(5),349-381
2 A. C. Lazer, P. J. McKenna, Largeamplitude periodic oscillations in suspension bridges: some new connections withnonlinear analysis[J], SIAM Review, 1990,32(1), 537-578
3 H. Brezis, L. Nirenberg, Positive solutions of nonlinear ellipiticequation involving critical sobolev exponents[J], Comm Pure Applmath 1983,36(1),437-477
4 C. A. Stuart, Self trapping of anelectromagnetic field and bifuraction from the essential spectum[J], Arch RatMechAnal, 1991, 113(5), 65-96
5 A. C. Lazer, P. J. McKenna, Globalbifurcation and a theorem of Tarantello[J], J Math Anal, 1994, 181 (6), 648-655
6 A. M. Micheletti, A. Pistotia,Multiplicity results for a fourth-order semilinear elliptic problem[J],Nonlinear Anal, 1998, 31(10), 895-908
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