@article{Li_Liu_Zhao_2008, title={Nodal solutions of perturbed elliptic problem}, volume={32}, url={https://apcz.umk.pl/TMNA/article/view/TMNA.2008.035}, abstractNote={Multiple nodal solutions are obtained for the elliptic problem $$ \alignat 2 -\Delta u&=f(x,\ u)+\varepsilon g(x,\ u)&\quad& \text{in } \Omega,\\ u&=0&\quad& \text{on } \partial \Omega , \endalignat $$ where $\varepsilon $ is a parameter, $\Omega $ is a smooth bounded domain in ${\mathbb R }^{N}$, $f\in C(\overline{\Omega }\times {\mathbb R })$, and $g\in C(\overline{\Omega }\times {\mathbb R })$. For a superlinear $C^{1}$ function $f$ which is odd in $u$ and for any $C^{1}$ function $g$, we prove that for any $j\in {\mathbb N}$ there exists $\varepsilon _{j}> 0$ such that if $|\varepsilon |\leq \varepsilon _{j}$ then the above problem possesses at least $j$ distinct nodal solutions. Except $C^{1}$ continuity no further condition is needed for $g$. We also prove a similar result for a continuous sublinear function $f$ and for any continuous function $g$. Results obtained here refine earlier results of S. J. Li and Z. L. Liu in which the nodal property of the solutions was not considered.}, number={1}, journal={Topological Methods in Nonlinear Analysis}, author={Li, Yi and Liu, Zhaoli and Zhao, Cunshan}, year={2008}, month={Sep.}, pages={49–68} }