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Global existence and multiplicity of positive solutions for anisotropic eigenvalue problems

  • Zhenhai Liu EMAIL logo and Nikolaos S. Papageorgiou
Published/Copyright: June 24, 2024
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Mathematica Slovaca
From the journal Mathematica Slovaca Volume 74 Issue 3

Abstract

We consider an eigenvalue problem driven by the anisotropic (p, q)-Laplacian and with a Carathéodory reaction which is (p(z) − 1)-sublinear as x → + ∞. We look for positive solutions. We prove an existence, nonexistence and multiplicity theorem which is global in the parameter λ > 0, that is, we prove a bifurcation-type theorem which describes in an exact way the changes in the set of positive solutions as the parameter λ varies on ℝ̊+ = (0, + ∞).

MSC 2010: Primary 35J20; 35J60
Keywords: Variable exponents; anisotropic regularity theory; eigenvalues; positive solutions; bifurcation-type result

The work was supported by Natural Science Foundation of Guangxi, China, Grant Nos. 2021GXNSFFA220001, 2023GXNSFAA026085 and the European Union’s Horizon 2020 Research and Innovation Programme under the Marie Sklodowska-Curie grant agreement No. 823731 CONMECH

  1. Communicated by Alberto Lastra

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Received: 2023-02-17
Accepted: 2023-09-26
Published Online: 2024-06-24
Published in Print: 2024-06-25

© 2024 Mathematical Institute Slovak Academy of Sciences

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https://doi.org/10.1515/ms-2024-0051
Keywords for this article
Variable exponents; anisotropic regularity theory; eigenvalues; positive solutions; bifurcation-type result

Articles in the same Issue

  1. On the Paley graph of a quadratic character
  2. A topological duality for tense modal pseudocomplemented De Morgan algebras
  3. Fibonacci numbers as mixed concatenations of Fibonacci and Lucas numbers
  4. A general formula in composition theory
  5. A nonlinear Filbert-like matrix with three free parameters: From linearity to nonlinearity
  6. On universality in short intervals for zeta-functions of certain cusp forms
  7. On asymptotics for lacunary partition functions
  8. Parallel surfaces of the non-lightlike solution of vortex filament equations
  9. New q-analogues of Van Hamme’s (F.2) supercongruence and of some related supercongruences
  10. Kneser-type oscillation theorems for second-order functional differential equations with unbounded neutral coefficients
  11. Approximation theorems via Pp-statistical convergence on weighted spaces
  12. Global existence and multiplicity of positive solutions for anisotropic eigenvalue problems
  13. Theoretical analysis of higher-order system of difference equations with generalized balancing numbers
  14. On a solvable difference equations system of second order its solutions are related to a generalized Mersenne sequence
  15. Positive bases, cones, Helly-type theorems
  16. Digital Jordan surfaces arising from tetrahedral tiling
  17. Influence of ideals in compactifications
  18. On the functions ωf and Ωf
  19. On the 𝓐-generators of the polynomial algebra as a module over the Steenrod algebra, I
  20. A bivariate distribution with generalized exponential conditionals
  21. A note on boundary feedback stabilization for degenerate parabolic equations in multi-dimensional domains
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