Comparison Principle for Elliptic Equations with Mixed Singular Nonlinearities

Abstract

We deal with existence and uniqueness of positive solutions of an elliptic boundary value problem modeled by

$$ \left \{\begin {array}{ll} \displaystyle -{\Delta }_{p} u= \frac {f}{u^{\gamma }} + g u^{q} & \text { in } {\Omega }, \\ u = 0 & \text {on } \partial {\Omega }, \end {array}\right . $$

where Ω is an open bounded subset of \(\mathbb {R}^{N}\) where Ω is an open bounded subset of \(\mathbb {R}^{N}\), Δpu := ÷(|∇u|p− 2u) is the usual p-Laplacian operator, γ ≥ 0 and 0 ≤ qp − 1; f and g are nonnegative functions belonging to suitable Lebesgue spaces.

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Open Access funding provided by Università degli Studi di Napoli Federico II.

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Correspondence to Francescantonio Oliva.

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Durastanti, R., Oliva, F. Comparison Principle for Elliptic Equations with Mixed Singular Nonlinearities. Potential Anal (2021). https://doi.org/10.1007/s11118-021-09906-3

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Keywords

  • Nonlinear elliptic equations
  • Singular elliptic equations
  • Sublinear elliptic equations
  • Uniqueness

Mathematics Subject Classification (2010)

  • 35J25
  • 35J60
  • 35J75
  • 35A01
  • 35A02