On a Kirchhoff type problems with potential well and indefinite potential

In this paper, we study the following Kirchhoff type problem:% \left\{\aligned&-\bigg(\alpha\int_{\bbr^3}|\nabla u|^2dx+1\bigg)\Delta u+(\lambda a(x)+a_0)u=|u|^{p-2}u&\text{ in }\bbr^3,\\% &u\in\h,\endaligned\right.\eqno{(\mathcal{P}_{\alpha,\lambda})}% where $4<p<6$, $\alpha$ and $\lambda$ are two positive parameters, a_0\in\bbr is a (possibly negative) constant and $a(x)\geq0$ is the potential well. By the variational method, we investigate the existence of nontrivial solutions to $(\mathcal{P}_{\alpha,\lambda})$. To our best knowledge, it is the first time that the nontrivial solution of the Kirchhoff type problem is found in the indefinite case. We also obtain the concentration behaviors of the solutions as $\lambda\to+\infty$.Comment: 1

Existence of solutions for a class of hemivariational inequality problems

AbstractIn this paper, we are concerned with the existence of solutions for a class of Hartman–Stampacchia type hemivariational inequalities by using the Clarke generalized directional derivative and the Galerkin approximation method. Two existence results of solutions for the generalized pseudomonotone mapping hemivariational inequality and elliptic hemivariational inequality are obtained

The Impact of Smoking Status on the Efficacy of Erlotinib in Patients with Advanced Non-small Cell Lung Cancer

Background and objective Erlotinib is a targeted treatment for advanced non-small cell lung cancer. Smoking status may be one of influencing factors of the efficacy of erlotinib. The aim of this study is to explore the impact of smoking status on the efficacy of erlotinib in patients with advanced non-small cell lung cancer. Methods Patients with nonsmall cell lung cancer who had been previously treated with at least one course of platinum based chemotherapy received 150 mg oral doses of erlotinib once daily until disease progression. Response rate, progression-free survival, overall survival were analyzed in the different smoking status groups. Kaplan-Meier method was used to analyze the survival rate. Results Fortyeight patients were enrolled into the study from December 2005 to September 2006. We followed up these patients until 28th December, 2008. Median follow up time was 30 months. The compliance rate was 100%. The response rate was 32.1% in the smoking group and 35% in the never smoking group (P=0.836); The median progression-free survival was 3 months and 9 months, respectively (P=0.033). The median overall survival was 5 months and 17 months, respectively (P=0.162). Conclusion Erlotinib is an effective drug for advanced non-small cell lung cancer patients with different smoking status. Progressionfree survival is better in the never smoking patients than the smoking patients