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Nonlinear nonhomogeneous singular problems
ID
Papageorgiou, Nikolaos S.
(
Author
),
ID
Rǎdulescu, Vicenţiu
(
Author
),
ID
Repovš, Dušan
(
Author
)
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Abstract
We consider a nonlinear Dirichlet problem driven by a nonhomogeneous differential operator with a growth of order ▫$(p-1)$▫ near ▫$+\infty$▫ and with a reaction which has the competing effects of a parametric singular term and a ▫$(p-1)$▫-superlinear perturbation which does not satisfy the usual Ambrosetti-Rabinowitz condition. Using variational tools, together with suitable truncation and strong comparison techniques, we prove a "bifurcation-type" theorem that describes the set of positive solutions as the parameter ▫$\lambda$▫ moves on the positive semiaxis. We also show that for every ▫$\lambda > 0$▫, the problem has a smallest positive solution ▫$u^\ast_\lambda$▫ and we demonstrate the monotonicity and continuity properties of the map ▫$\lambda \mapsto u^\ast_\lambda$▫.
Language:
English
Keywords:
singular term
,
superlinear perturbation
,
positive solution
,
nonhomogeneous differential operator
,
nonlinear regularity
,
minimal positive solutions
,
strong comparison principle
Work type:
Article
Typology:
1.01 - Original Scientific Article
Organization:
PEF - Faculty of Education
FMF - Faculty of Mathematics and Physics
Year:
2020
Number of pages:
art. 9 [31 str.]
Numbering:
Vol. 59, iss. 1
PID:
20.500.12556/RUL-116612
UDC:
517.956.2
ISSN on article:
0944-2669
DOI:
10.1007/s00526-019-1667-0
COBISS.SI-ID:
18823001
Publication date in RUL:
29.05.2020
Views:
1178
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480
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Record is a part of a journal
Title:
Calculus of variations and partial differential equations
Shortened title:
Calc. var. partial differ. equ.
Publisher:
Springer
ISSN:
0944-2669
COBISS.SI-ID:
3677529
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