Sign-changing solution and ground state solution for a class of (p,q)$(p,q)$-Laplacian equations with nonlocal terms on RN$\mathbb{R}^{N}$
نویسندگان
چکیده
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 a convergence property of such a solution uc,d as (c,d)→ 0. Finally, using the Lagrange multiplier method, we obtain a ground state solution of the equation and show that the energy of u is strictly larger than two times the ground state energy.
منابع مشابه
Existence of a ground state solution for a class of singular elliptic problem in RN$\mathbb{R}^{N}$
when p = , |f (x,u)| ≤ c(|u|+ |u|q–), < q≤ ∗ = N N– ,N ≥ , for the corresponding results onemay refer to Brézis [], Brézis and Nirenberg [], Bartsch andWillem [] and Capozzi, Fortunato and Palmieri []. Garcia and Alonso [] generalized Brézis, Nirenberg’s existence and nonexistence results to p-Laplace equation. Moreover, let us consider the following semilinear Schrödinger equation:
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