INFINITELY MANY SOLUTIONS FOR SOME NONLINEAR SUPERCRITICAL PROBLEMS WITH BREAK OF SYMMETRY

被引:3
作者
Candela, Anna Maria [1 ]
Salvatore, Addolorata [1 ]
机构
[1] Univ Bari Aldo Moro, Dipartimento Matemat, Via E Orabona 4, I-70125 Bari, Italy
关键词
quasilinear elliptic equation; weak Cerami-Palais-Smale condition; Ambrosetti-Rabinowitz condition; break of symmetry; perturbation method; supercritical growth; CRITICAL-POINT THEORY; ELLIPTIC-EQUATIONS;
D O I
10.7494/OpMath.2019.39.2.175
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this paper, we prove the existence of infinitely many weak bounded solutions of the nonlinear elliptic problem {-div(a(x, u, del u)) + A(t) (x, u, del u) = g(x, u) + h(x) in Omega, u = 0 on partial derivative Omega, where Omega subset of R-N is an open bounded domain, N >= 3, and A(x, t, xi), g(x, t), h(x) are given functions, with A(t) = partial derivative A/partial derivative t , a = del(xi)A, such that A(x, ., .) is even and g(x, .) is odd. To this aim, we use variational arguments and the Rabinowitz's perturbation method which is adapted to our setting and exploits a weak version of the Cerami-Palais-Smale condition. Furthermore, if A(x, t, xi) grows fast enough with respect to t, then the nonlinear term related to g(x, t) may have also a supercritical growth.
引用
收藏
页码:175 / 194
页数:20
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