We investigate the existence of solutions of the (p, q)-quasilinear elliptic problem {−Δpu−Δqu=g(x,u)+εh(x,u)inΩ,u=0on∂Ω, where Ω is an open bounded domain in ℝN, 1 < p < q < +∞, the nonlinearity g(x, u) behaves at infinity as |u|q−1, ε∈ ℝ and h∈ C(Ω ¯ × ℝ, ℝ). In spite of the possible lack of a variational structure of this problem, appropriate procedures and estimates allow us to prove the existence of at least one nontrivial solution for small perturbations.
An existence result for perturber (p, q)-quasilinear elliptic problems / Bartolo, Rossella; Maria Candela, Anna; Salvatore, Addolorata (TRENDS IN MATHEMATICS). - In: Recent Advances in Mathematical Analysis : Celebrating the 70th Anniversary of Francesco Altomare / [a cura di] Anna Maria Candela, Mirella Cappelletti Montano, Elisabetta Mangino. - STAMPA. - Cham, CH : Birkhäuser, 2023. - ISBN 978-3-031-20020-5. - pp. 135-164 [10.1007/978-3-031-20021-2_8]
An existence result for perturber (p, q)-quasilinear elliptic problems
Rossella Bartolo
;
2023-01-01
Abstract
We investigate the existence of solutions of the (p, q)-quasilinear elliptic problem {−Δpu−Δqu=g(x,u)+εh(x,u)inΩ,u=0on∂Ω, where Ω is an open bounded domain in ℝN, 1 < p < q < +∞, the nonlinearity g(x, u) behaves at infinity as |u|q−1, ε∈ ℝ and h∈ C(Ω ¯ × ℝ, ℝ). In spite of the possible lack of a variational structure of this problem, appropriate procedures and estimates allow us to prove the existence of at least one nontrivial solution for small perturbations.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
