Blow up of solutions for a r(x)-Laplacian Lam\'{e} equation with variable-exponent nonlinearities and arbitrary initial energy level

	Blow up of solutions for a r(x)-Laplacian Lam\'{e} equation with variable-exponent nonlinearities and arbitrary initial energy level
International Journal of Nonlinear Analysis and Applications
مقاله 34، دوره 13، شماره 1، خرداد 2022، صفحه 441-450 اصل مقاله (364.81 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.23671.2578
نویسنده
Mohammad Shahrouzi^*
Department of Mathematics, Jahrom University, Jahrom, Iran
چکیده
In this paper, we consider the nonlinear $r(x)-$Laplacian Lam'{e} equation $$ u_{tt}-\Delta_{e}u-div\big(\|\nabla u\|^{r(x)-2}\nabla u\big)+\|u_{t}\|^{m(x)-2}u_{t}=\|u\|^{p(x)-2}u $$ in a smoothly bounded domain $\Omega\subseteq R^{n},\ n\geq1$, where $r(.),\ m(.)$ and $p(.)$ are continuous and measurable functions. Under suitable conditions on variable exponents and initial data, the blow-up of solutions is proved with negative initial energy as well as positive.
کلیدواژه‌ها
blow-up؛ variable-exponent nonlinearities؛ elasticity operator؛ arbitrary initial energy
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