On a class of nonlinear problems involving a p(x)-Laplace type operator

Mihăilescu, Mihai

doi:10.1007/s10587-008-0011-1

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Introduction3

The Main Results1

Proof Of Theorem1

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Cited by 22 publications

(11 citation statements)

References 30 publications

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“…We point out the fact that similar results as the one of Theorems 2 and 3 were obtained by Mihȃilescu [8], in the case when in the left hand side of equations (13) and (14) we replace the anisotropic operator…”

Section: The Main Resultssupporting

confidence: 78%

See 1 more Smart Citation

Anisotropic Quasilinear Elliptic Equations With Variable Exponent

Mihăilescu¹,

Stancu‐Dumitru²

2012

Journal of the Korean Mathematical Society

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Section: The Main Resultssupporting

confidence: 78%

“…We recall that in [8,Lemma 4] it was proved that for any a, b > 0 and 0 < k < l the following inequality holds true…”

Section: Proof Of Theoremmentioning

confidence: 99%

Anisotropic Quasilinear Elliptic Equations With Variable Exponent

Mihăilescu¹,

Stancu‐Dumitru²

2012

Journal of the Korean Mathematical Society

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“…In [15], Mihȃilescu firstly studied the existence and multiplicity of weak solutions for a class of nonlinear problems with Dirichlet boundary condition of the form…”

Section: Introductionmentioning

confidence: 99%

Multiple Solutions for a Class of (P1(x), P2(x))-Laplacian Problems With Neumann Boundary Conditions

2018

Acta Univ. Apulensis Math. Inform.

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In this paper, we study the existence of solutions for a class of nonlinear Neumann problems with variable exponents of the form      −div (|∇u| p 1 (x)−2 + |∇u| p 2 (x)−2)∇u + |u| pmax(x)−2 u = λf (x, u) + µg(x, u) in Ω, ∂u ∂ν = 0 on ∂Ω, where Ω ⊂ R N , N ≥ 3 is a smooth bounded domain, ν is the outward unit normal to ∂Ω, λ, µ are positive parameters, p i ∈ C + (Ω), inf x∈Ω p max (x) > N , p max (x) = max{p 1 (x), p 2 (x)} for all x ∈ Ω, f, g : Ω × R → R are Carathéodory functions. Our proofs are essentially based on the three critical points theorem due to Ricceri [18].

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“…The p(x)-Laplacian operator possesses more complicated nonlinearities than the p-Laplacian operator, mainly due to the fact that it is not homogeneous. The study of various mathematical problems with variable exponent growth condition has been received considerable attention in recent years, we can for example refer to [1,4,17,24,29,35]. This great interest may be justified by their various physical applications.…”

Section: Introductionmentioning

confidence: 99%