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

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26220%2F25%3APU155154" target="_blank" >RIV/00216305:26220/25:PU155154 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.nonrwa.2024.104225" target="_blank" >https://doi.org/10.1016/j.nonrwa.2024.104225</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.nonrwa.2024.104225" target="_blank" >10.1016/j.nonrwa.2024.104225</a>

Result language
angličtina
Original language name
Singular non-autonomous (p,q)-equations with competing nonlinearities
Original language description
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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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