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A perturbed eigenvalue problem in exterior domain

  • Andrei Grecu
Veröffentlicht/Copyright: 9. August 2022
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Mathematica Slovaca
Aus der Zeitschrift Mathematica Slovaca Band 72 Heft 4

Abstract

Let Ω ⊂ RN (N ≥ 2) be a simply connected bounded domain, containing the origin, with C2 boundary denoted by ∂Ω. Denote by Ωext:=RN∖Ω¯the exterior of Ω. We consider the perturbed eigenvalue problem

− Δ p u − Δ q u = μ K ( x ) | u | p − 2 u  for  x ∈ Ω ext  u ( x ) = 0  for  x ∈ ∂ Ω u ( x ) → 0 ,  as  | x | → ∞ ,

where p, q ∈ (1,N), p≠qand K is a positive weight function defined on Ωext having the property that K ∈ L∞ (Ωext) ∩ LN/p (Ωext) . We show that the set of parameters μ for which the above eigenvalue problem possesses nontrivial weak solutions is exactly an unbounded open interval.

Keywords: Eigenvalue problem; weak solution; Nehari manifold; exterior domain
MSC 2010: 35J60; 35P99; 46E35

This work was supported by Research group of the project PN-III-P1-1.1-TE-2019-0456, University Politehnica of Bucharest, 060042 Bucharest, Romania.

  1. (Communicated by Alberto Lastra)

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Received: 2021-03-06
Accepted: 2021-07-07
Published Online: 2022-08-09
Published in Print: 2022-08-26

© 2022 Mathematical Institute Slovak Academy of Sciences

Artikel in diesem Heft

  1. Regular Papers
  2. Variants of Booleanness: Congruences of a partial frame versus those of its free frame
  3. Models, coproducts and exchangeability: Notes on states on Baire functions
  4. Inverse tangent series involving pell and pell-lucas polynomials
  5. A new family of two-variable polynomials based on hermite polynomials
  6. Decreasing property and complete monotonicity of two functions constituted via three derivatives of a function involving trigamma function
  7. On the solvability of a fourth-order differential evolution equation on singular cylindrical domain in R4
  8. Investigation of an implicit Hadamard fractional differential equation with Riemann-Stieltjes integral boundary condition
  9. Stability criteria for systems of two first-order linear ordinary differential equations
  10. A perturbed eigenvalue problem in exterior domain
  11. On extensions of bilinear maps
  12. Refinement of seminorm and numerical radius inequalities of semi-Hilbertian space operators
  13. Weighted composition operators from the Besov space into nth weighted type spaces
  14. Fuzzy ideal topological vector spaces
  15. Partial actions on convergence spaces
  16. On quasi-small loop groups
  17. Topologies generated by symmetric porosity on normed spaces
  18. The Alpha Power Rayleigh-G family of distributions
  19. An alternative for Laplace Birnbaum-Saunders distribution
  20. Existence of positive solutions for boundary value problems with p-Laplacian operator
https://doi.org/10.1515/ms-2022-0065
Schlagwörter für diesen Artikel
Eigenvalue problem; weak solution; Nehari manifold; exterior domain

Artikel in diesem Heft

  1. Regular Papers
  2. Variants of Booleanness: Congruences of a partial frame versus those of its free frame
  3. Models, coproducts and exchangeability: Notes on states on Baire functions
  4. Inverse tangent series involving pell and pell-lucas polynomials
  5. A new family of two-variable polynomials based on hermite polynomials
  6. Decreasing property and complete monotonicity of two functions constituted via three derivatives of a function involving trigamma function
  7. On the solvability of a fourth-order differential evolution equation on singular cylindrical domain in R4
  8. Investigation of an implicit Hadamard fractional differential equation with Riemann-Stieltjes integral boundary condition
  9. Stability criteria for systems of two first-order linear ordinary differential equations
  10. A perturbed eigenvalue problem in exterior domain
  11. On extensions of bilinear maps
  12. Refinement of seminorm and numerical radius inequalities of semi-Hilbertian space operators
  13. Weighted composition operators from the Besov space into nth weighted type spaces
  14. Fuzzy ideal topological vector spaces
  15. Partial actions on convergence spaces
  16. On quasi-small loop groups
  17. Topologies generated by symmetric porosity on normed spaces
  18. The Alpha Power Rayleigh-G family of distributions
  19. An alternative for Laplace Birnbaum-Saunders distribution
  20. Existence of positive solutions for boundary value problems with p-Laplacian operator
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