Ground state sign-changing solutions for a class of generalized quasilinear Schrödinger equations with a Kirchhoff-type perturbation

Sign-changing solutions of critical quasilinear Kirchhoff-Schr\”{o}dinger-Poisson system with logarithmic nonlinearity

“…Lately, under suitable condition of f , Chen and Tang [11] applied some new analytical techniques and non-Nehari manifold method investigated the existence of ground state signchanging solutions for the following quasilinear Schrödinger equations with a Kirchhoff-type perturbation:…”

“…Arguing by contradiction, we assume that (I λ b,µ ) (u b,µ ) = 0, then there exist δ > 0 and τ > 0 such that Let ε := min{c λ b,µ − c λ , τ σ 8 } and S δ = B(u b,µ , δ), according to Lemma 2.3 in [11], there exists…”

The existence of sign-changing solution for a class of quasilinear Schrödinger–Poisson systems via perturbation method

“…Deng, Peng, and Wang in [13] obtained a sign-changing minimizer of (1.4) by adopting the minimization argument. Chen et al in [9] proved the existence of sign-changing solutions with two nodal domains for (1.4) with a Kirchhoff-type perturbation by using Miranda's theorem and deformation lemma. Deng, Peng, and Yan in [14,15] investigated a generalized quasilinear Schrödinger equation with critical exponents by using a change of variables and variational argument.…”

“…This argument mainly shows that there is a minimizer of I constrained on M 0 and then verifies that the minimizer is a critical point of I via quantitative deformation lemma and degree theory. By using the method, the sign-changing solution for some nonlocal equations is constructed (see [1,9,10,17,18,21,[33][34][35]). The Choquard equation was studied by Ghimenti and Schaftingen in [18].…”

“…The Kirchhoff equation was investigated by Figueiredo and Nascimento in [17], Tang and Chen in [35], and Shuai in [33]. The quasilinear Schrödinger equations with a Kirchhoff-type perturbation were discussed by Li, Zhu, and Liang in [21] and Chen et al in [9].…”