Existence of solutions for Solitons type equations : Derrick's Problem with twice p-laplacian

Abdelkader Dellal (1) , Johnny Henderson (2) , Abdelghani Ouahab (3)

1 Université Ibn Khaldoun de Tiaret = University of Tiaret
2 Department of Mathematics, Baylor University
3 UDL - جامعة جيلالي اليابس [سيدي بلعباس، الجزائر] = Université Djillali Liabès [Sidi Bel Abbès, Algérie] = Djillali Liabes University [Sidi Bel Abbès, Algeria]

In this paper we study a class of Lorentz invariant nonlinear field equations in several space dimensions. The fields are characterized by a topological invariant, which we call the charge. We prove the existence of a static solution which minimizes the energy among the configurations with nontrivial charge. In this spirit, a considerable amount of work has been done by V. Benci and collaborators and a model equation proposed in [2] will be the topic of this paper. The main purpose is to obtain soliton-like solutions with twice p-Laplacian.

Mots clés: Soliton; variational calculus; splitting lemma. AMS (MOS) Subject Classifications:35C08; 35J35; 35J60

Domaines: Mathématiques [math]

Abdelkader Dellal, Johnny Henderson, Abdelghani Ouahab. Existence of solutions for Solitons type equations : Derrick's Problem with twice p-laplacian. CARI 2022, Oct 2022, Tunis, Tunisia. ⟨hal-03712446⟩