On An Elliptic Equation With Concave and Convex Nonlinearities
On An Elliptic Equation With Concave and Convex Nonlinearities
复制标题
DOI：
10.1090/s0002-9939-1995-1301008-2
复制
发表时间：
1995-11
期刊：
影响因子：
--
通讯作者：
T. Bartsch;M. Willem
中科院分区：
文献类型：
--
作者：
T. Bartsch;M. Willem
我们研究了具有狄利克雷边界条件的 R(N) 的开界域 Omega 子集中的半线性椭圆方程 -Delta u=lambdau(q-2)u+muu(p-2)u；这里 1 0 且 mu 是 R 的一个元素，任意存在一个解序列 (upsilon(k))，其负能量收敛到 0，因为 k --> 无穷大。此外，对于 mu > 0 和 lambda 任意，存在一系列具有无限能量的解。这回答了 Ambrosetti、Brezis 和 Cerami 的问题。主要成分是一个新的临界点定理，它保证了在有界范围内偶函数存在无限多个临界值。我们还可以处理强不定泛函并获得一阶哈密顿系统的类似结果。
We study the semilinear elliptic equation -Delta u=lambdau(q-2)u+muu(p-2)u in an open bounded domain Omega subset of R(N) with Dirichlet boundary conditions; here 1 0 and mu is an element of R arbitrary there exists a sequence (upsilon(k)) of solutions with negative energy converging to 0 as k --> infinity. Moreover, for mu > 0 and lambda arbitrary there exists a sequence of solutions with unbounded energy. This answers a question of Ambrosetti, Brezis and Cerami. The main ingredient is a new critical point theorem, which guarantees the existence of infinitely many critical values of an even functional in a bounded range. We can also treat strongly indefinite functionals and obtain similar results for first-order Hamiltonian systems.