High energy solutions of general Kirchhoff type equations without the Ambrosetti-Rabinowitz type condition

In this article, we study the following general Kirchhoff type equation: where and is a superlinear subcritical term. By using the Pohozǎev manifold, we obtain the existence of high energy solutions of the aforementioned equation without the well-known Ambrosetti-Rabinowitz type condition.

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Published inAdvances in nonlinear analysis Vol. 12; no. 1; pp. 18 - 34
Main Authors Zhang, Jian, Liu, Huize, Zuo, Jiabin
Format Journal Article
LanguageEnglish
Published De Gruyter 01.04.2023
Subjects
35J60
35R11
35S15
47G20
high energy solution
Kirchhoff type equation
Pohozǎev manifold
variational method
Online AccessGet full text
ISSN2191-950X
2191-950X
DOI10.1515/anona-2022-0311

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Abstract In this article, we study the following general Kirchhoff type equation: where and is a superlinear subcritical term. By using the Pohozǎev manifold, we obtain the existence of high energy solutions of the aforementioned equation without the well-known Ambrosetti-Rabinowitz type condition.
AbstractList In this article, we study the following general Kirchhoff type equation: −M∫R3∣∇u∣2dxΔu+u=a(x)f(u)inR3,-M\left(\mathop{\int }\limits_{{{\mathbb{R}}}^{3}}| \nabla u{| }^{2}{\rm{d}}x\right)\Delta u+u=a\left(x)f\left(u)\hspace{1em}{\rm{in}}\hspace{0.33em}{{\mathbb{R}}}^{3}, where infR+M>0{\inf }_{{{\mathbb{R}}}^{+}}M\gt 0 and ff is a superlinear subcritical term. By using the Pohozǎev manifold, we obtain the existence of high energy solutions of the aforementioned equation without the well-known Ambrosetti-Rabinowitz type condition.
In this article, we study the following general Kirchhoff type equation: where and is a superlinear subcritical term. By using the Pohozǎev manifold, we obtain the existence of high energy solutions of the aforementioned equation without the well-known Ambrosetti-Rabinowitz type condition.
In this article, we study the following general Kirchhoff type equation: − M ∫ R 3 ∣ ∇ u ∣ 2 d x Δ u + u = a ( x ) f ( u ) in R 3 , -M\left(\mathop{\int }\limits_{{{\mathbb{R}}}^{3}}| \nabla u{| }^{2}{\rm{d}}x\right)\Delta u+u=a\left(x)f\left(u)\hspace{1em}{\rm{in}}\hspace{0.33em}{{\mathbb{R}}}^{3}, where inf R + M > 0 {\inf }_{{{\mathbb{R}}}^{+}}M\gt 0 and f f is a superlinear subcritical term. By using the Pohozǎev manifold, we obtain the existence of high energy solutions of the aforementioned equation without the well-known Ambrosetti-Rabinowitz type condition.
Author Liu, Huize
Zhang, Jian
Zuo, Jiabin
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Snippet In this article, we study the following general Kirchhoff type equation: where and is a superlinear subcritical term. By using the Pohozǎev manifold, we obtain...
In this article, we study the following general Kirchhoff type equation: − M ∫ R 3 ∣ ∇ u ∣ 2 d x Δ u + u = a ( x ) f ( u ) in R 3 , -M\left(\mathop{\int...
In this article, we study the following general Kirchhoff type equation: −M∫R3∣∇u∣2dxΔu+u=a(x)f(u)inR3,-M\left(\mathop{\int }\limits_{{{\mathbb{R}}}^{3}}|...
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SubjectTerms 35J60
35R11
35S15
47G20
high energy solution
Kirchhoff type equation
Pohozǎev manifold
variational method
Title High energy solutions of general Kirchhoff type equations without the Ambrosetti-Rabinowitz type condition
URI https://www.degruyter.com/doi/10.1515/anona-2022-0311
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