Journal
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
Volume 59, Issue 1, Pages -Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s00526-019-1667-0
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Funding
- Slovenian Research Agency [P1-0292, J1-8131, N1-0114, N1-0064, N1-0083]
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We consider a nonlinear Dirichlet problem driven by a nonhomogeneous differential operator with a growth of order ( p- 1) near+8 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. moves on the positive semiaxis. We also show that for every. > 0, the problem has a smallest positive solution u *. and we demonstrate the monotonicity and continuity properties of the map lambda -> u(lambda)*.
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