کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5024731 | 1470453 | 2017 | 29 صفحه PDF | دانلود رایگان |
In this paper, motivated by recent works on the study of the equations which model the electrostatic MEMS devices, we study the quasilinear elliptic equation involving a singular nonlinearity {â(rα|uâ²(r)|βuâ²(r))â²=λrγf(r)(1âu(r))2,râ(0,1),0â¤u(r)<1,râ(0,1),uâ²(0)=u(1)=0. According to the choice of the parameters α,β and γ, the differential operator which we are dealing with corresponds to the radial form of the Laplacian, the p-Laplacian and the k-Hessian. In this work we present conditions over which we can assert regularity for solutions, including the case λ=λâ, where λâ is a critical value for the existence of solutions. Moreover, we prove that whenever the critical solution is regular, there exists another solution of mountain pass type for λ close to the critical one. In addition, we use the Shooting Method to prove uniqueness of solutions for λ in a neighborhood of 0.
Journal: Nonlinear Analysis: Theory, Methods & Applications - Volume 148, January 2017, Pages 1-29