Existence and nonexistence results for generalized quasilinear Schrödinger equations of Kirchhoff type in ℝ<sup>3</sup>

Shen, Liejun

doi:10.1080/00036811.2019.1569225

Cited by 3 publications

(2 citation statements)

References 38 publications

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“…At first, let us briefly review the predecessors' pioneering works about the problem [16][17][18][19][20]. However, to the best of our knowledge, there are no works involving Eq.…”

Section: Related Work and Main Resultsmentioning

confidence: 99%

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On the asymptotically cubic generalized quasilinear Schrödinger equations with a Kirchhoff-type perturbation

Qiu

Cheng

et al. 2023

Front. Phys.

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In this paper, we consider the non-existence and existence of solutions for a generalized quasilinear Schrödinger equation with a Kirchhoff-type perturbation. When the non-linearity h(u) shows critical or supercritical growth at infinity, the non-existence result for a quasilinear Schrödinger equation is proved via the Pohožaev identity. If h(u) shows asymptotically cubic growth at infinity, the existence of positive radial solutions for the quasilinear Schrödinger equation is obtained when b is large or equal to 0 and b is equal to 0 by the variational methods. Moreover, some properties are established as the parameter b tends to be 0.

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“…At first, let us briefly review the predecessors' pioneering works about the problem [16][17][18][19][20]. However, to the best of our knowledge, there are no works involving Eq.…”

Section: Related Work and Main Resultsmentioning

confidence: 99%

“…We should mention that our results are new since we focus on the asymptotically cubic case. Compared with [16,19,20], we know that in Theorem 1.1, our non-linear term in the autonomy problem Eq. 1.1 is supercritical, so we invoke the Pohožaev-type identity.…”

Section: Our Contributions and Methodsmentioning

confidence: 99%

On the asymptotically cubic generalized quasilinear Schrödinger equations with a Kirchhoff-type perturbation

Qiu

Cheng

et al. 2023

Front. Phys.

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Sign‐changing solution to a critical p‐Kirchhoff equation with potential vanishing at infinity in ℝN

Shen

2024

Math Methods in App Sciences

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In this paper, we study the critical ‐Laplacian equation of Kirchhoff type where is the Kirchhoff function, with and is a parameter, , and the potentials and vanish at infinity. Under some suitable assumptions on , by using the constraint minimization approach, we obtain a least energy sign‐changing solution to this problem if is large enough and show the energy of is strictly larger than twice that of the ground state solutions. Moreover, by considering a wider class of and , we exploit the truncation argument to find a nontrivial solution if is sufficiently large via some analytic skills.

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Sign-Changing Solutions to a N-Kirchhoff Equation with Critical Exponential Growth in $$\mathbb {R}^N$$

Shen

2021

Bull. Malays. Math. Sci. Soc.

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Existence and nonexistence results for generalized quasilinear Schrödinger equations of Kirchhoff type in ℝ³

Cited by 3 publications

References 38 publications

On the asymptotically cubic generalized quasilinear Schrödinger equations with a Kirchhoff-type perturbation

On the asymptotically cubic generalized quasilinear Schrödinger equations with a Kirchhoff-type perturbation

Sign‐changing solution to a critical p‐Kirchhoff equation with potential vanishing at infinity in ℝN

Sign-Changing Solutions to a N-Kirchhoff Equation with Critical Exponential Growth in $$\mathbb {R}^N$$

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Existence and nonexistence results for generalized quasilinear Schrödinger equations of Kirchhoff type in ℝ3

Cited by 3 publications

References 38 publications

On the asymptotically cubic generalized quasilinear Schrödinger equations with a Kirchhoff-type perturbation

On the asymptotically cubic generalized quasilinear Schrödinger equations with a Kirchhoff-type perturbation

Sign‐changing solution to a critical p‐Kirchhoff equation with potential vanishing at infinity in ℝN

Sign-Changing Solutions to a N-Kirchhoff Equation with Critical Exponential Growth in $$\mathbb {R}^N$$

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Existence and nonexistence results for generalized quasilinear Schrödinger equations of Kirchhoff type in ℝ³