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 AltomareSTAMPA. - [s.l], 2023. - pp. 135-164 [10.1007/978-3-031-20021-2_8]
An existence result for perturber (p, q)-quasilinear elliptic problems
Rossella Bartolo
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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.| File | Dimensione | Formato | |
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