当前位置: X-MOL 学术Ukr. Math. J. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
On the p ( X )-Kirchhoff-Type Equation Involving the p ( X )-Biharmonic Operator via the Genus Theory
Ukrainian Mathematical Journal ( IF 0.5 ) Pub Date : 2020-11-21 , DOI: 10.1007/s11253-020-01836-4
S. Taarabti , Z. El Allali , K. Ben Haddouch

The paper deals with the existence and multiplicity of nontrivial weak solutions for the p(x)-Kirchhofftype problem

$$ {\displaystyle \begin{array}{c}-M\left(\underset{\Omega}{\int}\frac{1}{p(x)}{\left|\Delta u\right|}^{p(x)} dx\right){\Delta}_{p(x)}^2u=f\left(x,u\right)\kern0.6em \mathrm{in}\kern0.48em \Omega, \\ {}u=\Delta u=0\kern0.48em \mathrm{on}\kern0.48em \mathrm{\partial \Omega }.\end{array}} $$

By using the variational approach and the Krasnosel’skii genus theory, we prove the existence and multiplicity of solutions for the p(x)-Kirchhoff-type equation.



中文翻译:

基于类理论的涉及p(X)-双调和算子的p(X)-Kirchhoff-型方程

本文讨论了px)-Kirchhoff型问题的非平凡弱解的存在性和多重性。

$$ {\ displaystyle \ begin {array} {c} -M \ left(\ underset {\ Omega} {\ int} \ frac {1} {p {x)} {\ left | \ Delta u \ right |} ^ {p(x)} dx \ right){\ Delta} _ {p(x)} ^ 2u = f \ left(x,u \ right)\ kern0.6em \ mathrm {in} \ kern0.48em \ Omega ,\\ {} u = \ Delta u = 0 \ kern0.48em \ mathrm {on} \ kern0.48em \ mathrm {\ partial \ Omega}。\ end {array}} $$

通过使用变分方法和Krasnosel'skii类理论,我们证明了px)-Kirchhoff型方程的解的存在性和多重性。

更新日期:2020-11-22
down
wechat
bug