Existence of solutions for a problem with multiple singular weighted p-Laplacians and vanishing potentials
Alves, Maria Jose
Assuncao, Ronaldo B.
Texas State University, Department of Mathematics
This work establishes the existence of positive solutions to a quasilinear singular elliptic equations involving the (p-q)-Laplacian operator with singularities and a vanishing potential. We adapt the penalization method developed by del Pino and Felmer and we consider an auxiliary problem whose corresponding functional satisfies the geometry of the mountain-pass theorem; then, we prove that the Palais-Smale sequences are bounded in a Sobolev space; after that, we show that the auxiliary problem has a solution. Finally, we use the Moser iteration scheme to obtain an appropriate estimate and we conclude that the solution to the auxiliary problem is also a solution to the original problem.
Quasilinear elliptic equations with singularities, (p-q)-Laplacian, Variational methods, Singular elliptic equation, Vanishing potential, Penalization method, Moser iteration scheme
Alves, M. J., & Assunção, R. B. (2022). Existence of solutions for a problem with multiple singular weighted p-Laplacians and vanishing potentials. <i>Electronic Journal of Differential Equations, 2022</i>(43), pp. 1-25.
Attribution 4.0 International