Constant sign and nodal solutions for superlinear (<i>p</i>, <i>q</i>)–equations with indefinite potential and a concave boundary term

Zhang

2020

Bound Value Probl

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We consider a nonlinear Dirichlet problem driven by a general nonhomogeneous differential operator and with a reaction exhibiting the combined effects of a parametric singular term plus a Carathéodory perturbation $f(z,x,y)$ f ( z , x , y ) which is only locally defined in $x \in {\mathbb {R}} $ x ∈ R . Using the frozen variable method, we prove the existence of a positive smooth solution, when the parameter is small.

Section: The Frozen Variable Methodsmentioning

confidence: 73%

“…Such operators arise often in the mathematical models of physical processes and recently there have been published several works dealing with equations driven by such operators. We mention the works of Bobkov-Tanaka [3], Papageorgiou-Zhang [26,27], Rădulescu [29], Ragusa-Tachikawa [30].…”

Section: Corollary 3 We Have Cmentioning

confidence: 99%

Nonlinear nonhomogeneous Dirichlet problems with singular and convection terms

Zhang

2020

Bound Value Probl

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“…We also mention the isotropic works of the authors [21,22] on singular equations driven by the ( p, q)-Laplacian and the p-Laplacian, respectively. Finally, related works to the topic can be found in the papers of Ambrosio [1], Ambrosio-Rȃdulescu [2], Liu-Motreanu-Zeng [15], Papageorgiou-Zhang [23], Ragusa-Tachikawa [25], Zeng-Bai-Gasiński-Winkert [28,29] and the references therein.…”

Section: ( )mentioning

confidence: 99%

Positive Solutions for Singular Anisotropic (p, q)-Equations

Winkert

2021

J Geom Anal

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In this paper, we consider a Dirichlet problem driven by an anisotropic (p, q)-differential operator and a parametric reaction having the competing effects of a singular term and of a superlinear perturbation. We prove a bifurcation-type theorem describing the changes in the set of positive solutions as the parameter moves. Moreover, we prove the existence of a minimal positive solution and determine the monotonicity and continuity properties of the minimal solution map.

“…Finally, we mention recent papers which are very close to our topic dealing with certain types of nonhomogeneous and/or singular problems. We refer to Papageorgiou-Rȃdulescu-Repovš [26,28], Papageorgiou-Zhang [22] and Ragusa-Tachikawa [30].…”

Section: Theorem 11 If Hypotheses H(a)mentioning

confidence: 99%

(p, q)-Equations with Singular and Concave Convex Nonlinearities

Winkert

2020

Appl Math Optim

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We consider a nonlinear Dirichlet problem driven by the (p, q)-Laplacian with $$1<q<p$$ 1 < q < p . The reaction is parametric and exhibits the competing effects of a singular term and of concave and convex nonlinearities. We are looking for positive solutions and prove a bifurcation-type theorem describing in a precise way the set of positive solutions as the parameter varies. Moreover, we show the existence of a minimal positive solution and we study it as a function of the parameter.