Rad HAZU, Matematičke znanosti, Vol. 27 (2023), 133-142.

A GROUND STATE SOLUTION FOR A NONHOMOGENEOUS ELLIPTIC KIRCHHOFF TYPE PROBLEM INVOLVING CRITICAL GROWTH AND HARDY TERM

Safia Benmansour, Nadjet Yagoub and Atika Matallah

Laboratoire d'analyse et controle des équations aux dérivées partielles, Université Djilali, Liabes Sidi Bel Abbès, Algérie
e-mail: manadjet222@gmail.com

Ecole supérieure de management de Tlemcen, Laboratoire d'analyse et controle des équations aux dérivées partielles, Université Djilali, Liabes Sidi Bel Abbès, Algérie
e-mail: atika_matallah@yahoo.fr

Abstract.   This paper concerns singular elliptic Kirchhof’s equations whose nonlinearity has a critical growth and contains an inhomogeneous perturbation in a regular bounded domain of R³. To explore the existence of a ground state solution, we rely on various techniques related to variational methods and the Nehari decomposition.

2020 Mathematics Subject Classification.   35J20, 35IJ60, 47J30.

Key words and phrases.   Variational methods, critical growth, Hardy term, singular elliptic problems, Kirchhoff equations.

DOI: https://doi.org/10.21857/m8vqrtgr09

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