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On the antimaximum principle for the p-Laplacian and its sublinear perturbations

Author

Listed:
  • Vladimir Bobkov

    (Ufa Federal Research Centre, RAS)

  • Mieko Tanaka

    (Tokyo University of Science)

Abstract

We investigate qualitative properties of weak solutions of the Dirichlet problem for the equation $$-\Delta _p u = \lambda \,m(x)|u|^{p-2}u+ \eta \,a(x)|u|^{q-2}u+ f(x)$$ - Δ p u = λ m ( x ) | u | p - 2 u + η a ( x ) | u | q - 2 u + f ( x ) in a bounded domain $$\Omega \subset \mathbb {R}^N$$ Ω ⊂ R N , where $$q 1$$ p > 1 solutions of the unperturbed problem satisfy the antimaximum principle in a right neighborhood of the first eigenvalue of the p-Laplacian provided $$m,f \in L^\gamma (\Omega )$$ m , f ∈ L γ ( Ω ) with $$\gamma >N$$ γ > N . For completeness, we also investigate the existence of solutions.

Suggested Citation

  • Vladimir Bobkov & Mieko Tanaka, 2023. "On the antimaximum principle for the p-Laplacian and its sublinear perturbations," Partial Differential Equations and Applications, Springer, vol. 4(3), pages 1-38, June.
  • Handle: RePEc:spr:pardea:v:4:y:2023:i:3:d:10.1007_s42985-023-00235-1
    DOI: 10.1007/s42985-023-00235-1
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    References listed on IDEAS

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    1. Mieko Tanaka, 2012. "Existence Results for Quasilinear Elliptic Equations with Indefinite Weight," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-31, July.
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