Nonlinear Eigenvalues for a Quasilinear Elliptic System in Orlicz–Sobolev Spaces

Regularity, positivity and asymptotic vanishing of solutions of a φ-Laplacian

“…The existence of nontrivial solutions of equations in the divergence form is proved in [5]via a classical Lagrange rule. This result is somewhat motivated by the ideas in [14,Theorem 3.1]. The proof of [21,Theorem 2.2] follows similar lines but in a different, nonhomogeneous context.…”

Existence and multiplicity of solutions for a class of quasilinear elliptic systems in Orlicz-Sobolev spaces

“…To the best of our knowledge, there are few papers considering the existence and multiplicity of solutions for systems like (1.1) except for [23,34,36]. In [23], Huentutripay-Manásevich studied an eigenvalue problem to the following system:    −div(φ 1 (|∇u|)∇u) = λF u (x, u, v) in Ω, −div(φ 2 (|∇v|)∇v) = λF v (x, u, v) in Ω, u = v = 0 on ∂Ω, where the function F has the form F(x, u, v) = A 1 (x, u) + b(x)Γ 1 (u)Γ 2 (v) + A 2 (x, v).…”

“…In [23], Huentutripay-Manásevich studied an eigenvalue problem to the following system:    −div(φ 1 (|∇u|)∇u) = λF u (x, u, v) in Ω, −div(φ 2 (|∇v|)∇v) = λF v (x, u, v) in Ω, u = v = 0 on ∂Ω, where the function F has the form F(x, u, v) = A 1 (x, u) + b(x)Γ 1 (u)Γ 2 (v) + A 2 (x, v).…”

Blow-up rates of large solutions for a ϕ-Laplacian problem with gradient term

“…Recent advances in problems involving elliptic operators motivate the study of (1.1) (see [8,11,[14][15][16]). For example, in [16] the scalar problem − div φ(|∇u|) ∇u |∇u| = B (x, u) in Ω was considered, where φ is an odd increasing homeomorphism of R, and Ω is a bounded domain in R N .…”