Publication detail

Singular non-autonomous (p,q)-equations with competing nonlinearities

PAPAGEORGIOU, N. QIN, D. RADULESCU, V.

Original Title

Singular non-autonomous (p,q)-equations with competing nonlinearities

Type

journal article in Web of Science

Language

English

Original Abstract

We consider a parametric non-autonomous (p,q)-equation with a singular term and competing nonlinearities, a parametric concave term and a Carathéodory perturbation. We consider the cases where the perturbation is (p−1)-linear and where it is (p−1)-superlinear (but without the use of the Ambrosetti–Rabinowitz condition). We prove an existence and multiplicity result which is global in the parameter λ>0 (a bifurcation type result). Also, we show the existence of a smallest positive solution and show that it is strictly increasing as a function of the parameter. Finally, we examine the set of positive solutions as a function of the parameter (solution multifunction). First, we show that the solution set is compact in C01(Ω̄) and then we show that the solution multifunction is Vietoris continuous and also Hausdorff continuous as a multifunction of the parameter.

Keywords

(p-1)-linear and (p-1)-superlinear perturbations; Minimal solution; Nonlinear regularity theory; Solution multifunction; Truncations and comparisons

Authors

PAPAGEORGIOU, N.; QIN, D.; RADULESCU, V.

Released

2. 2. 2025

ISBN

1878-5719

Periodical

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS

Year of study

81

Number

104225

State

Kingdom of the Netherlands

Pages count

25

URL

https://doi.org/10.1016/j.nonrwa.2024.104225

BibTex

@article{BUT194033,
  author="Nikolaos S. {Papageorgiou} and Dongdong {Qin} and Vicentiu {Radulescu}",
  title="Singular non-autonomous (p,q)-equations with competing nonlinearities",
  journal="NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS",
  year="2025",
  volume="81",
  number="104225",
  pages="25",
  doi="10.1016/j.nonrwa.2024.104225",
  issn="1878-5719",
  url="https://doi.org/10.1016/j.nonrwa.2024.104225"
}