具有不定位势和凹非线性项的Robin问题的解的多重性

Multiple Solutions for Robin Problem with Indefinite Potential and Concave Nonlinearities

研究非线性项由凹项λ|u|^(q−2)(其中1<q<2)和在无穷远处以超线性或渐近线性增长的连续项f(x,u)组成的半线性不定位势的Robin问题,在不同情形下,运用变分法、截断技巧和Morse理论,得到了该问题的多重解的存在性结果.

We investigate semilinear Robin problem with indefinite potential and right-hand-side nonlinearity which is exhibits-sublinear term of the form λ|u|q-2, 1 < q < 2(concave term), and a continuous term f(x, u) which is superlinear or asymptotically linear at infinity respectively. Under some different conditions, we establish some existence results of multiple solutions by using variational methods and truncation techniques combined with the Morse theory.