Document Type
Article
Publication Date
1-19-2026
Published In
Boundary Value Problems
Abstract
We are concerned with the existence of solutions of (p, q)-Laplacian problems that include nonlinear perturbation terms in both the differential equations and the boundary. Using variational methods and critical point theory, we prove the existence of weak solutions for the nonlinear problem when the nonlinearities involved remain asymptotically below the infimum of the set of eigenvalues of the (p, q)-Laplacian problem with weights and a spectral parameter present in both the differential equation and the boundary. Additionally, we establish an existence result for the nonlinear problem when the nonlinearities involved remain asymptotically below the first Steklov-Neumann eigenvalue-line, which is a line connecting the first Steklov and first Neumann eigenvalues for q-Laplacian problems with weights and a spectral parameter present either in the differential equation or on the boundary.
Keywords
(p q)-Laplacian, Nonlinear perturbations, Nonlinear boundary condition, Nonresonance, Steklov-Neumann eigenvalue-line, Critical point, Variational methods
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.
Recommended Citation
E. Lopera, Nsoki Mavinga, and D. Sánchez.
(2026).
"Nonresonance For Problems Involving (p, q)-Laplacian Equations With Nonlinear Perturbations".
Boundary Value Problems.
Volume 2026,
Issue 1.
DOI: 10.1186/s13661-025-02183-8
https://works.swarthmore.edu/fac-math-stat/349