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## Existence and multiplicity of weak solutions for gradient-type systems with oscillatory nonlinearities on the Sierpiński gasket

#### Haiffa Muhsan B. Alrikabi [1] , Ghasem A. Afrouzi [2] , Mohsen Alimohammady [3]

In this paper, we establish the existence and multiplicity results of solutions for parametric quasi-linear systems of the gradient-type on the Sierpiński gasket is proved. Our technical approach is based on variational methods and critical points theory and on certain analytic and geometrical properties of the Sierpiński fractal. Indeed, using a consequence of the local minimum theorem due to Bonanno, the Palais-Smale condition cut off upper at $r$, and the Palais-Smale condition for the Euler functional we investigate the existence of one and two solutions for our problem under algebraic conditions on the nonlinear part. Moreover by applying a different three critical point theorem due to Bonanno and Marano we guarantee the existence of third solution for our problem.
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Primary Language en Mathematics Mathematics Orcid: 0000-0002-9615-8480Author: Haiffa Muhsan B. Alrikabi Orcid: 0000-0001-8794-3594Author: Ghasem A. Afrouzi (Primary Author) Orcid: 0000-0001-8358-9962Author: Mohsen Alimohammady Publication Date : October 8, 2019
 Bibtex @research article { hujms629912, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe University}, year = {2019}, volume = {48}, pages = {1461 - 1478}, doi = {}, title = {Existence and multiplicity of weak solutions for gradient-type systems with oscillatory nonlinearities on the Sierpiński gasket}, key = {cite}, author = {Alrikabi, Haiffa Muhsan B. and Afrouzi, Ghasem A. and Alimohammady, Mohsen} } APA Alrikabi, H , Afrouzi, G , Alimohammady, M . (2019). Existence and multiplicity of weak solutions for gradient-type systems with oscillatory nonlinearities on the Sierpiński gasket. Hacettepe Journal of Mathematics and Statistics , 48 (5) , 1461-1478 . Retrieved from https://dergipark.org.tr/en/pub/hujms/issue/49321/629912 MLA Alrikabi, H , Afrouzi, G , Alimohammady, M . "Existence and multiplicity of weak solutions for gradient-type systems with oscillatory nonlinearities on the Sierpiński gasket". Hacettepe Journal of Mathematics and Statistics 48 (2019 ): 1461-1478 Chicago Alrikabi, H , Afrouzi, G , Alimohammady, M . "Existence and multiplicity of weak solutions for gradient-type systems with oscillatory nonlinearities on the Sierpiński gasket". Hacettepe Journal of Mathematics and Statistics 48 (2019 ): 1461-1478 RIS TY - JOUR T1 - Existence and multiplicity of weak solutions for gradient-type systems with oscillatory nonlinearities on the Sierpiński gasket AU - Haiffa Muhsan B. Alrikabi , Ghasem A. Afrouzi , Mohsen Alimohammady Y1 - 2019 PY - 2019 N1 - DO - T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 1461 EP - 1478 VL - 48 IS - 5 SN - 2651-477X-2651-477X M3 - UR - Y2 - 2018 ER - EndNote %0 Hacettepe Journal of Mathematics and Statistics Existence and multiplicity of weak solutions for gradient-type systems with oscillatory nonlinearities on the Sierpiński gasket %A Haiffa Muhsan B. Alrikabi , Ghasem A. Afrouzi , Mohsen Alimohammady %T Existence and multiplicity of weak solutions for gradient-type systems with oscillatory nonlinearities on the Sierpiński gasket %D 2019 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 48 %N 5 %R %U ISNAD Alrikabi, Haiffa Muhsan B. , Afrouzi, Ghasem A. , Alimohammady, Mohsen . "Existence and multiplicity of weak solutions for gradient-type systems with oscillatory nonlinearities on the Sierpiński gasket". Hacettepe Journal of Mathematics and Statistics 48 / 5 (October 2019): 1461-1478 . AMA Alrikabi H , Afrouzi G , Alimohammady M . Existence and multiplicity of weak solutions for gradient-type systems with oscillatory nonlinearities on the Sierpiński gasket. Hacettepe Journal of Mathematics and Statistics. 2019; 48(5): 1461-1478. Vancouver Alrikabi H , Afrouzi G , Alimohammady M . Existence and multiplicity of weak solutions for gradient-type systems with oscillatory nonlinearities on the Sierpiński gasket. Hacettepe Journal of Mathematics and Statistics. 2019; 48(5): 1478-1461.