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- W2896738905 abstract "In this paper, we investigate abstract critical point theorems for continuously Gâteaux differentiable functionals satisfying the Cerami condition via the generalized Ekeland variational principle developed by C.-K. Zhong. As applications of our results, under certain assumptions, we show the existence of at least one or two weak solutions for nonlinear elliptic equations with variable exponents [ -operatorname{div} (varphi(x, nabla u)) + V(x) |u|^{p(x)-2} u = lambda f(x,u) quad textrm{in } mathbb{R}^{N}, ] where the function $varphi(x,v)$ is of type $|v|^{p(x)-2}v$ with a continuous function $p colon mathbb{R}^{N} to (1,infty)$, $V colon mathbb{R}^{N} to (0,infty)$ is a continuous potential function, $lambda$ is a real parameter, and $f colon mathbb{R}^{N} times mathbb{R} to mathbb{R}$ is a Caratheodory function. Especially, we localize precisely the intervals of $lambda$ for which the above equation admits at least one or two nontrivial weak solutions by applying our critical points results." @default.
- W2896738905 created "2018-10-26" @default.
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- W2896738905 date "2019-02-01" @default.
- W2896738905 modified "2023-10-06" @default.
- W2896738905 title "Critical Points Theorems via the Generalized Ekeland Variational Principle and its Application to Equations of $p(x)$-Laplace Type in $mathbb{R}^{N}$" @default.
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- W2896738905 doi "https://doi.org/10.11650/tjm/181004" @default.
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