Complex Variables and Elliptic Equations ( IF 0.6 ) Pub Date : 2021-04-27 , DOI: 10.1080/17476933.2021.1916918 Qi Zhang 1 , Die Hu 1
In this paper, we discuss the existence of multiple solutions of the generalized quasilinear Schrödinger equation of Kirchhoff-type where b>0 is a parameter, . In preceding approaches, the order of the nonlinear term about t at infinity is usually supposed to be higher than . But in this paper, this condition is not necessary. Under weaker condition , where is the primitive function of , , we get the existence of infinitely many solutions of the equation. Our work can be regarded as the extension of those such as [J. Zhang et al. Existence of multiple solutions of Kirchhoff type equation with sign-changing potential. Appl Math Comput. 2014;242:491–499] and related works.
中文翻译:
一类基尔霍夫型拟线性薛定谔方程解的存在性
在本文中,我们讨论了基尔霍夫型广义拟线性薛定谔方程的多重解的存在性其中b > 0 是一个参数,. 在前面的方法中,非线性项的阶大约在无穷远处的t通常应该高于. 但在本文中,这个条件不是必须的。在较弱的条件下, 在哪里是的原始函数,,我们得到方程的无限多解的存在性。我们的工作可以看作是诸如[J. 张等人。具有变符号势的基尔霍夫型方程的多重解的存在性。应用数学计算。2014;242:491–499] 和相关著作。