We consider a Dirichlet problem driven by general nonlinear, nonhomogeneous differential operator. The reaction has the competing effects of singular term and parametric perturbation which is superlinear sign-changing. Using variational tools from critical point theory together with truncation comparison techniques, we show that for all small values parameter, at least two positive smooth solut...

Abstract It is well known that classical optical cavities can exhibit localized phenomena associated with scattering resonances, leading to numerical instabilities in approximating the solution. This result be established via ‘quasimodes resonances’ argument from black box framework. Those concentrate at inner boundary of cavity and are called whispering gallery modes. In this paper we investig...