J. Nonl. Mod. Anal., 6 (2024), pp. 71-87.
Published online: 2024-03
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We consider the biharmonic equation $∆^2u− (a+b\int_{\mathbb{R}^5} |∇u|^2 dx) ∆u + V (x)u = f(u),$ where $V(x)$ and $f(u)$ are continuous functions. By using a perturbation approach and the symmetric mountain pass theorem, the existence and multiplicity of solutions for this equation are obtained, and the power-type case $f(u) = |u|^ {p−2}u$ is extended to $p ∈ (2, 10),$ where it was assumed $p ∈ (4, 10)$ in many papers.
}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2024.71}, url = {http://global-sci.org/intro/article_detail/jnma/22967.html} }We consider the biharmonic equation $∆^2u− (a+b\int_{\mathbb{R}^5} |∇u|^2 dx) ∆u + V (x)u = f(u),$ where $V(x)$ and $f(u)$ are continuous functions. By using a perturbation approach and the symmetric mountain pass theorem, the existence and multiplicity of solutions for this equation are obtained, and the power-type case $f(u) = |u|^ {p−2}u$ is extended to $p ∈ (2, 10),$ where it was assumed $p ∈ (4, 10)$ in many papers.