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Existence of solutions for a $(p,q)$-Laplace equation with Steklov boundary conditions | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 10، دوره 14، شماره 7، مهر 2023، صفحه 119-122 اصل مقاله (340.7 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2022.7160 | ||
| نویسندگان | ||
| Abdolrahman Razani؛ Farzaneh Safari* | ||
| Department of Mathematics, Imam Khomeini International University, Qazvin, Iran | ||
| تاریخ دریافت: 27 اسفند 1400، تاریخ بازنگری: 03 تیر 1401، تاریخ پذیرش: 21 شهریور 1401 | ||
| چکیده | ||
| Here, the existence of at least one nontrivial solution for the $(p,q)$-Laplacian problem \[ \left\{ \begin{array}{lc} div(|\nabla u|^{p-2}\nabla u)+div(|\nabla u|^{q-2}\nabla u)=f(x,u)\qquad & x\in \Omega, \\ \\ |\nabla u|^{p-2}\frac{\partial u}{\partial n}+ |\nabla u|^{q-2}\frac{\partial u}{\partial n}=g(x,u) & x\in \partial \Omega \end{array} \right. \] is done, where $ \Omega$ is a bounded domain in $\mathbb{R}^N, N\geq 3$ and $q, p\geq 2$, via variational methods. | ||
| کلیدواژهها | ||
| $(p؛ q)$-Laplace equation؛ Steklov boundary conditions؛ Mountain Pass Theorem | ||
| مراجع | ||
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[1] M. Badiale and E. Serra, Semilinear Elliptic Equations for Beginners, Existence results via the variational approach, Springer, 2011. [2] M.A. Ragusa, A. Razani and F. Safari, Existence of radial solutions for a p(x)-Laplacian Dirichlet problem, Adv. Differential Equations 2021 (2021), no. 1, 1–14. [3] F. Safari and A. Razani, Existence of positive radial solutions for Neumann problem on the Heisenberg group, Bound. Value Probl. 2020 (2020), no. 1, 1–14. [4] F. Safari and A. Razani, Nonlinear nonhomogeneous Neumann problem on the Heisenberg group, Appl. Anal. 101 (2020), no. 7, 2387–2400. [5] F. Safari and A. Razani, Existence of radial solutions of the Kohn-Laplacian problem, Complex Var. Elliptic Equ. 67 (2022), no. 2, 259–273. [6] F. Safari and A. Razani, Positive weak solutions of a generalized supercritical Neumann problem, Iran J. Sci. Technol. Trans. Sci. 44 (2020), no. 6, 1891–1898, [7] F. Safari and A. Razani, Radial solutions for a general form of a p-Laplace equation involving nonlinearity terms, Complex Var. Elliptic Equ. (2021), 1–11. https://doi.org/10.1080/17476933.2021.1991331. [8] F. Safari and A. Razani, Existence of radial solutions for a weighted p-biharmonic problem with Navier boundary condition on the Heisenberg group, Math. Slovaca 72 (2022), no. 3, 677–692. | ||
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