A new mixed variational–hemivariational problem is introduced, $a(u,v-u)+b(v-u,\lambda )+\phi \left(v\right)-\phi \left(u\right)+J^0(Tu;Tv-Tu)\ge {(f,v-u)}_X,$ $b(u,\mu -\lambda )-\psi \left(\mu \right)+\psi \left(\lambda \right)-{\Psi }^0(R\lambda ;R\mu -R\lambda )\le 0,$ ($v\in X,$ $\mu \in \Lambda \subseteq Y$), focusing on its well-posedness. We are looking for a pair solution $(u,\lambda )\in X\times \Lambda$ working into a Hilbert spaces framework. Some particular cases with applications in mechanics are highlighted. A special attention is payed to a particular case leading to a mixed variational–hemivariational problem with penalty term. In order to illustrate the theory, we provide examples such that $X,Y,\Lambda ,a,b,\phi ,\psi ,J,\Psi ,R,T$ fulfill the working hypotheses.

引入了一个新的混合变分-半变分问题， $\mathrm{一种}(你,v-你)+乙(v-你,\lambda )+\phi \left(v\right)-\phi \left(你\right)+J^0(吨你;吨v-吨你)\ge {(F,v-你)}_X,$ $乙(你,\mu -\lambda )-\psi \left(\mu \right)+\psi \left(\lambda \right)-{\Psi }^0(\mathrm{电阻}\lambda ;\mathrm{电阻}\mu -\mathrm{电阻}\lambda )\le 0,$ ($v\in X,$ $\mu \in \Lambda \subseteq 是$)，专注于其适定性。我们正在寻找配对解决方案$(你,\lambda )\in X\times \Lambda$进入希尔伯特空间框架。突出显示了一些在力学中应用的特殊案例。特别注意导致带有惩罚项的混合变分-半变分问题的特定情况。为了说明理论，我们提供了一些例子，这样$X,是,\Lambda ,\mathrm{一种},乙,\phi ,\psi ,J,\Psi ,\mathrm{电阻},吨$ 满足工作假设。