Quasilinear Choquard equations involving N-Laplacian and critical exponential nonlinearity

In the present paper, we study a class of quasilinear Choquard equations involving N-Laplacian and the nonlinearity with the critical exponential growth. We discuss the existence of positive solutions of such equations.

Existence and regularity of time-dependent pullback attractors for the non-autonomous nonclassical diffusion equations

In this paper, we prove the existence and regularity of pullback attractors for non-autonomous nonclassical diffusion equations with nonlocal diffusion when the nonlinear term satisfies critical exponential growth and the external force term $h \in L_{l o c}^{2}(\mathbb {R} ; H^{-1}(\Omega )).$ Under some appropriate assumptions, we establish the existence and uniqueness of the weak solution in the time-dependent space $\mathcal {H}_{t}(\Omega )$ and the existence and regularity of the pullback attractors.

Ground state solutions for a Kirchhoff type elliptic systems involving critical exponential growth nonlinearities

The aim of this paper is to study the ground state solution for a Kirchhoff type elliptic systems without the Ambrosetti-Rabinowitz condition.