In this article, we apply the Nehari manifold method to study the Kirchhoff type equation

In this article, we investigate the asymptotic behavior of positive ground state solutions, as α→∞, for the following Hénon type system −∆u = 2p p+ q |x|αup−1vq , −∆v = 2q p+ q |x|αupvq−1, in B1(0) with zero boundary condition, where B1(0) ⊂ RN (N ≥ 3) is the unit ball centered at the origin, p, q > 1, p+ q < 2∗ = 2N/(N − 2). We show that both components of the ground solution pair (u, v) conce...

In the paper, we investigate the least energy sign-changing solution and the ground state solution of a class of (p,q)-Laplacian equations with nonlocal terms on RN . Applying the constraint variational method, the quantitative deformation lemma, and topological degree theory, we see that the equation has one least energy sign-changing solution u. Moreover, we regard c, d as parameters and give...

In this paper, we generalize the definitions of approximately inner $C_0$-groups and their ground states to the two- parameter case and study necessary and sufficient conditions for a state to be ground state. Also we prove that any approximately inner two- parameter $C_0$--group must have at least one ground state. Finally some applications are given.

The aim of this paper is to study radial symmetry properties for ground state solutions of elliptic equations involving a regional fractional Laplacian, namely (−∆)ρ u+ u = f(u) in R, for α ∈ (0, 1). (1) In [9], the authors proved that problem (1) has a ground state solution. In this work we prove that the ground state level is achieved by a radially symmetry solution. The proof is carried out ...