Details

Autor(en) / Beteiligte

• Sahu, Abhilash
• Prem Prasad, M. Guru

Titel

Non‐homogeneous p‐Laplacian equations on the Sierpinski gasket

Ist Teil von

• Mathematical methods in the applied sciences, 2023-04, Vol.46 (6), p.6545-6557

Ort / Verlag

Freiburg: Wiley Subscription Services, Inc

Erscheinungsjahr

2023

Quelle

Wiley Online Library Journals Frontfile Complete

Beschreibungen/Notizen

• Let S$$ \mathcal{S} $$ be the Sierpiński gasket in ℝ2$$ {\mathbb{R}}^2 $$ and S0$$ {\mathcal{S}}_0 $$ denote the boundary of S$$ \mathcal{S} $$. In this paper, we study the following non‐homogeneous p$$ p $$‐Laplacian equation −Δpu=λ|u|q−2u+finS\S0u=0onS0,$$ {\displaystyle \begin{array}{cc}\hfill -{\Delta}_pu& =\lambda {\left|u\right|}^{q-2}u+f\kern.5em \mathrm{in}\kern3.0235pt \mathcal{S}\backslash {\mathcal{S}}_0\hfill \\ {}\hfill u& =0\kern3.0235pt \mathrm{on}\kern3.0235pt {\mathcal{S}}_0,\hfill \end{array}} $$ where p,q,λ$$ p,q,\lambda $$ are real numbers such that λ>0,1<p<q$$ \lambda >0,1<p<q $$ and the function f:S→ℝ$$ f:\mathcal{S}\to \mathbb{R} $$ is suitably chosen. The existence of at least two nontrivial weak solutions to the above non‐homogeneous equation on the Sierpiński gasket will be established.