Quasilinear Schrodinger-Poisson system with exponential and logarithmic nonlinearities

In this paper, we consider the following quasilinear Schrodinger-Poisson system with exponential and logarithmic nonlinearities {-Delta u+phi u=vertical bar u vertical bar(p-2)u log vertical bar u vertical bar(2) + lambda f(u), in Omega, -Delta phi-epsilon(4)Delta(4)phi = u(2), in Omega, u = phi = 0, on partial derivative Omega, where 4 < p < +infinity, epsilon, lambda > 0 are parameters, Delta(4)phi = div(vertical bar del phi vertical bar(2)del phi), Omega subset of R-2 is a bounded domain, and f has exponential critical growth. By adopting the reduction argument and a truncation technique, we prove for every epsilon > 0, the above system admits at least one pair of nonnegative solutions (u(epsilon,lambda),phi(epsilon,lambda)) for lambda > 0 large. Furthermore, we research the asymptotical behavior of solutions with respect to the parameters epsilon and lambda. The novelty of this system is the intersection among the quasilinear term, logarithmic term, and exponential critical term. These results are new and improve some existing results in the literature.

Automated summary

This paper considers the existence and asymptotic behavior of solutions to a quasilinear Schrödinger-Poisson system with exponential and logarithmic nonlinearities, proving the existence of at least one nonnegative pair of solutions and improving some existing results. The novelty of the system lies in the intersection among the quasilinear, logarithmic, and exponential critical terms.