In this paper, we study the following elliptic boundary value problem: $$ \textstyle\begin{cases} -\Delta u+V(x)u=f(x, u),\quad x\in \Omega , \\ u=0, \quad x \in \partial \Omega , \end{cases} $$ where $\Omega \subset {\mathbb {R}}^{N}$ is a bounded domain with smooth boundary ∂Ω, and f is allowed to be sign-changing and is of sublinear growth near infinity in u. For both cases that $V\in L^{N/2}(\Omega )$ with $N\geq 3$ and that $V\in C(\Omega , \mathbb {R})$ with $\inf_{\Omega }V(x)>-\infty $ , we establish a sequence of nontrivial solutions converging to zero for above equation via a new critical point theorem.

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具有正负号变势和一般非线性的亚线性椭圆型方程的多重性结果

在本文中，我们研究以下椭圆边值问题：$$ \ textstyle \ begin {cases--Delta u + V（x）u = f（x，u），\ quad x \ in \ Omega，\\ u = 0，\ quad x \ in \ partial \ Omega，\ end {cases} $$其中$ \ Omega \ subset {\ mathbb {R}} ^ {N} $是具有光滑边界∂Ω的有界域，并且f允许符号改变，并且在u中具有无限大的亚线性增长。对于这两种情况，$ V \ in L ^ {N / 2}（\ Omega）$和$ N \ geq 3 $以及$ V \ in C（\ Omega，\ mathbb {R}）$和$ \ inf_ { \ Omega} V（x）>-\ infty $，我们通过一个新的临界点定理为上述方程建立了一个收敛为零的非平凡序列。