Multiple solutions for elliptic equations involving a general operator in divergence form

Bisci, Giovanni Molica; Repovš, Dušan

doi:10.5186/aasfm.2014.3909

Cited by 24 publications

(1 citation statement)

References 15 publications

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“…These results apply to special forms of differential equations, characterized by different abstract conditions on nonlinearities and nonstandard ( p , q ) growth of such equation. In addition, we refer to Acerbi and Mingione, 7 Ru˙z̆ic̆ka, 8 Chen et al, 9 Harjulehto et al, 10 and Molica Bisci and Repovš 11 for a deeper analysis on properties, modeling, and application of variable exponent spaces to smart fluids (see also Bgelein et al 12 ). More specifically, for electrorheological fluids, we refer to Ru˙z̆ic̆ka, 8 Mihǎsilescu and Rǎdulescu, 13 and Rajagopal and Ru˙z̆ic̆ka 14,15 ; for thermorheological fluids, we refer to Antontsev and Rodrigues 16 .…”

Section: Introductionmentioning

confidence: 99%

On (p(x), q(x))‐Laplace equations in ℝN without Ambrosetti‐Rabinowitz condition

Nastasi

2021

Math Methods in App Sciences

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In the present work, we consider a (p(x), q(x))‐elliptic equation describing the behavior of a double‐phase anisotropic problem which has relevance in electrorheological fluid applications. The analysis leads to the existence of weak (nonnegative) solutions in the special case of potential terms with critical frequency and a superlinear reaction term. In order to prove the existence result, we combine critical point theory of mountain pass type with related topological and variational methods. Basically, the approach is variational, but we do not impose any Ambrosetti‐Rabinowitz type condition for the superlinearity of the reaction. More specifically, we apply the Euler‐Lagrange functional approach to the variational formulation of the above‐mentioned model problem. We note that we work in the whole space ℝN and so we have to consider non‐compact embeddings. This aspect constitutes an additional difficulty in our study.

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Section: Introductionmentioning

confidence: 99%

On (p(x), q(x))‐Laplace equations in ℝN without Ambrosetti‐Rabinowitz condition

Nastasi

2021

Math Methods in App Sciences

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Fractional Schrödinger Equation in Bounded Domains and Applications

Chrouda

2017

Mediterr. J. Math.

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Multiple sign-changing radially symmetric solutions in a general class of quasilinear elliptic equations

Alves

Gonçalves

Silva

2015

Z. Angew. Math. Phys.

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In this paper we prove that the equation −(r α φ(|u ′ (r)|)u ′ (r)) ′ = λr γ f (u(r)), 0 < r < R, where α, γ, R are given real numbers, φ : (0, ∞) → (0, ∞) is a suitable twice differentiable function, λ > 0 is a real parameter and f : R → R is continuous, admits an infinite sequence of signchanging solutions satisfying u ′ (0) = u(R) = 0. The function f is required to satisfy tf (t) > 0 for t = 0. Our technique explores fixed point arguments applied to suitable integral equations and shooting arguments. Our main result extends earlier ones in the case φ is in the form φ(t) = |t| β for an appropriate constant γ.

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Multiple solutions for elliptic equations involving a general operator in divergence form

Cited by 24 publications

References 15 publications

On (p(x), q(x))‐Laplace equations in ℝN without Ambrosetti‐Rabinowitz condition

On (p(x), q(x))‐Laplace equations in ℝN without Ambrosetti‐Rabinowitz condition

Fractional Schrödinger Equation in Bounded Domains and Applications

Multiple sign-changing radially symmetric solutions in a general class of quasilinear elliptic equations

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