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Multiple solutions for quasilinear elliptic problems with nonlinear boundary conditions.

Chung, Nguyen Thanh — 2008

Electronic Journal of Differential Equations (EJDE) [electronic only]

Existence of weak solutions for a nonuniformly elliptic nonlinear system in $ℝ^{N}$ .

Chung, Nguyen Thanh — 2008

Electronic Journal of Differential Equations (EJDE) [electronic only]

Existence of infinitely many solutions for degenerate and singular elliptic systems with indefinite concave nonlinearities.

Nguyen Thanh Chung — 2011

Electronic Journal of Differential Equations (EJDE) [electronic only]

Existence of solutions for a class of Kirchhoff type problems in Orlicz-Sobolev spaces

Nguyen Thanh Chung — 2015

Annales Polonici Mathematici

We consider Kirchhoff type problems of the form ⎧ -M(ρ(u))(div(a(|∇u|)∇u) - a(|u|)u) = K(x)f(u) in Ω ⎨ ⎩ ∂u/∂ν = 0 on ∂Ω where $Ω \subset ℝ^{N}$ , N ≥ 3, is a smooth bounded domain, ν is the outward unit normal to ∂Ω, $ρ (u) = \int_{Ω} (Φ (| \nabla u |) + Φ (| u |)) d x$ , M: [0,∞) → ℝ is a continuous function, $K \in L^{\infty} (Ω)$ , and f: ℝ → ℝ is a continuous function not satisfying the Ambrosetti-Rabinowitz type condition. Using variational methods, we obtain some existence and multiplicity results.

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Currently displaying 1 – 4 of 4

Multiple solutions for quasilinear elliptic problems with nonlinear boundary conditions.

Existence of weak solutions for a nonuniformly elliptic nonlinear system in ℝ N .

Existence of infinitely many solutions for degenerate and singular elliptic systems with indefinite concave nonlinearities.

Existence of solutions for a class of Kirchhoff type problems in Orlicz-Sobolev spaces

Existence of weak solutions for a nonuniformly elliptic nonlinear system in $ℝ^{N}$ .