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- W2902014300 abstract "In this paper we investigate the existence and multiplicity of homoclinic solutions for the following damped vibration problem: DS $$ ddot{u}+q(t) dot{u}-L(t)u+W_{u}(t,u)=0, $$ where $q:mathbb{R}rightarrowmathbb{R}$ is a continuous function, $Lin C(mathbb{R}, mathbb{R}^{n^{2}})$ is a symmetric and positive definite matrix for all $tinmathbb{R}$ and $Win C^{1}(mathbb{R}timesmathbb{R}^{n}, mathbb{R})$ . The novelty of this paper is that, assuming $lim_{|t|rightarrow+infty }Q(t)=+infty$ ( $Q(t)=int_{0}^{t} q(s) ,ds$ ) and L is coercive at infinity, we establish one new compact embedding theorem. Subsequently, supposing that W satisfies the global Ambrosetti–Rabinowitz condition, we obtain some new criterion to guarantee the existence of homoclinic solution of (DS) using the mountain pass theorem. Moreover, if W is even, then (DS) has infinitely many homoclinic solutions. Recent results in the literature are generalized and significantly improved." @default.
- W2902014300 created "2018-12-11" @default.
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- W2902014300 date "2018-12-01" @default.
- W2902014300 modified "2023-09-24" @default.
- W2902014300 title "Fast homoclinic solutions for damped vibration problems with superquadratic potentials" @default.
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- W2902014300 doi "https://doi.org/10.1186/s13661-018-1103-y" @default.
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