Degree Theory for Operators of Monotone Type and Nonlinear Elliptic Equations With Inequality Constraints

By Sergiu Aizicovici, Nikolaos S. Papageorgiou, V. Staicu. 2008

242 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/00cc8baea7569cba6b6532e79053df3512269b5b

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In Applied Mathematics

In Computational Theory and Mathematics

In Mechanics of Materials

Citations in the corpus

A bifurcation-type theorem for singular nonlinear elliptic equations (2015, background): “By virtue of Claim 2, as in Aizicovici-Papageorgiou-Staicu [1] (see the proof of Proposition 29), we can find ρ ∈ (0, 1) small s.t. (72) ψ̂λ(u0) inf[ ψ̂λ(u) : ||u− u0|| = ρ ] = η̂ρ.”
Nonlinear nonhomogeneous singular problems (2019, background): “Assume that X is a Banach space, φ ∈ C(X,R) satisfies the C-condition, u0, u1 ∈ X, ||u1 − u0||X > ρ > 0, max{φ(u0), φ(u1)} < inf {φ(u) : ||u− u0||X = ρ} = mρ and c = inf γ∈Γ max 06t<1 φ(γ(t)) with Γ = {γ ∈ C([0, 1], X) : γ(0) = u0, γ(1) = u1}.”
Qualitative Phenomena for Some Classes of Quasilinear Elliptic Equations with Multiple Resonance (2014, result): “Concerning the map Ar we can state the following well-known result (see Aizicovici, Papageorgiou & Staicu [1]).”
Existence of multiple solutions with precise sign information for superlinear Neumann problems (2009, unknown): “[2] (see the Proof of Proposition 31), we obtain h = gy p−1 with g ∈ L∞(Z)+, ξ ≤ g(z) ≤ η̂ a.”
Multiple Solutions for Nonlinear Coercive Problems with a Nonhomogeneous Differential Operator and a Nonsmooth Potential (2012, unknown): “To this end, let c = { γ ∈ C([0, 1];C1 0( )) : γ (0) = v0, γ (1) = u0}.”
On a Class of Parametric (p, 2)-equations (2016, unknown): “So, we can find small ρ ∈ (0, 1) such that φλ(û−) 6 φλ(û+) < inf[φλ(u) : ||u− û+|| = ρ] = m λ ρ , ||û− − û+|| > ρ (26) (see Aizicovici, Papageorgiou and Staicu [1], proof of Proposition 29).”
Positive solutions for nonlinear parametric singular Dirichlet problems (2018, unknown): “Because of (49), we can find ρ ∈ (0, 1) small such that ϕ̃λ(uλ) inf{ϕ̃λ(u) : ||u− uλ|| = ρ} = m̃λ(50) (see Aizicovici, Papageorgiou & Staicu [1], proof of Proposition 29).”
Positive solutions for perturbations of the Robin eigenvalue problem plus an indefinite potential (2017, background): “REFERENCES [1] S. Aizicovici, N. S. Papageorgiou and V. Staicu, Degree theory for operators of monotone type and nonlinear elliptic equations with inequality constraints, Memoirs Amer.”