Dwivedi, GauravGauravDwivediTyagi, JagmohanJagmohanTyagi2025-08-312025-08-312023-03-0110.1002/mana.2021000692-s2.0-85142362906https://d8.irins.org/handle/IITG2025/25753We establish the existence of a solution to the following problem: (Formula presented.) where (Formula presented.), is a smooth and bounded domain and (Formula presented.), where (Formula presented.) is the ith eigenvalue of symmetric matrix (Formula presented.). We assume that (Formula presented.) and (Formula presented.) are parameters. Moreover, we assume that (Formula presented.) if (Formula presented.) and (Formula presented.) if (Formula presented.). We use variational arguments and an iterative technique to prove our results.falsegradient nonlinearity | higher order elliptic equations | second Hessian | variational methodsArticle152226161056-1070March 20231arJournal1WOS:000888618700001