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We study the existence of bound and ground states for a class of nonlinear elliptic systems in $mathbb{R}^N$. These equations involve critical power nonlinearities and Hardy-type singular potentials, coupled by a term containing up to critical powers. More precisely, we find ground states either the positive coupling parameter $ u$ is large or $ u$ is small under suitable assumptions on the other parameters of the problem. Furthermore, bound states are found as Mountain-Pass-type critical points of the underlying functional constrained on the Nehari manifold. Our variational approach improves some known results and allows us to cover range of parameters which have not been considered previously.
In this paper, we are concerned with the existence and asymptotic behavior of minimizers for a minimization problem related to some quasilinear elliptic equations. Firstly, we proved that there exist minimizers when the exponent $q$ equals to the cri
We analyze free energy functionals for macroscopic models of multi-agent systems interacting via pairwise attractive forces and localized repulsion. The repulsion at the level of the continuous description is modeled by pressure-related terms in the
In this paper we study the existence of solutions of thedegererate elliptic system.
We study ground state solutions for linear and nonlinear elliptic PDEs in $mathbb{R}^n$ with (pseudo-)differential operators of arbitrary order. We prove a general symmetry result in the nonlinear case as well as a uniqueness result for ground states
It is established existence of bound and ground state solutions for quasilinear elliptic systems driven by (phi 1, phi 2)-Laplacian operator. The main feature here is to consider quasilinear elliptic systems involving both nonsingular nonlinearities