CAJ | 학술논문

本文研究了一类带有非线性边界条件的拟线性椭圆方程.在比常用的经典条件弱的假设条件下,得到该方程所对应的能量泛函存在有界Palais-Smale序列.然后,利用山路引理,得到该方程非平凡解的存在性.最后,给出一个例子,说明所给的条件比经典条件弱.
본문연구료일류대유비선성변계조건적의선성타원방정.재비상용적경전조건약적가설조건하,득도해방정소대응적능량범함존재유계Palais-Smale서렬.연후,이용산로인리,득도해방정비평범해적존재성.최후,급출일개례자,설명소급적조건비경전조건약.
In this paper, we investigate a class of quasilinear elliptic equations with nonlinear boundary condition. The existence of bounded Palais-Smale sequences for the corresponding functional of the equation is obtained under hypotheses weaker than those commonly used in the literature. Then,by applying Mountain Pass Lemma, the existence of nontrivial solution is confirmed. Furthermore,we give an example which illustrates that the condition we give is more general than the superquadratic growth condition.