Existence of three nontrivial solutions for semilinear elliptic equations on ℝ<Superscript><Emphasis Type="Italic">N</Emphasis></Superscript>

We establish the existence theorem of three nontrivial solutions for a class of semilinear elliptic equation on ℝ ^N by using variational theorems of mixed type due to Marino and Saccon and linking theorem.  

Fractional <Emphasis Type="Italic">p</Emphasis>-Laplacian Equations with Subcritical and Critical Exponential Growth Without the Ambrosetti–Rabinowitz Condition

The main purpose of this paper is to investigate the existence of nontrivial solutions to a class of quasilinear non-local problems which do not satisfy the Ambrosetti–Rabinowitz (AR) condition where the nonlinear terms are superlinear at 0 and of subcritical or critical exponential growth (subcritical polynomial growth) at \(\infty \). Some existence results for nontrivial solution are obtained using mountain pass theorem combined with the fractional Moser–Trudinger inequality.  

带色散项的周期可积Hunter-Saxton方程的波的破裂

本文考虑一个带色散项的可积Hunter-Saxton方程的周期柯西问题.首先,我们得出该模型的强解的一个精确的爆破机制.其次,利用守恒量和特征方法,分别建立了有限时间内强解的爆破发生的充分条件.最后,给出了强解的爆破率.  

一类拟线性椭圆方程的非平凡解

运用环绕理论和对称型山路理论对一类具有次临界多项式增长和次临界指数增长的$p$-Laplacian方程建立一个非平凡解(无穷多个非平凡解)的存在性结果.