Positive solutions for nonlinear elliptic problems with dependence on the gradient

By Leszek Gasinski, Nikolaos S. Papageorgiou. 2017

59 citations recorded by the source corpus.

Abstract We consider a quasilinear Neumann problem with a differential operator and a reaction term, both dependent on u and Du . Using topological methods together with suitable truncation and comparison techniques, we show that the problem has at least one positive smooth solution.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c3612247d027b8d2fa6261c3673a2998c72a2215

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Patrick Winkert
2. Leszek Gasinski
3. Nikolaos S. Papageorgiou
4. Vicentiu D. Rădulescu
5. Dušan D. Repovš
6. Shengda Zeng
7. Zhenhai Liu
8. Dumitru Motreanu

In Computational Theory and Mathematics

1. Patrick Winkert
2. Nikolaos S. Papageorgiou
3. Leszek Gasinski
4. Vicentiu D. Rădulescu
5. Dušan D. Repovš
6. Shengda Zeng
7. Zhenhai Liu
8. Dumitru Motreanu

In Mathematical Physics

1. Leszek Gasinski
2. Patrick Winkert
3. Vicentiu D. Rădulescu
4. Dušan D. Repovš
5. Nikolaos S. Papageorgiou
6. Shengda Zeng
7. Zhenhai Liu
8. Dumitru Motreanu

Citations in the corpus

• Existence and uniqueness results for double phase problems with convection term (2019, methodology): “For other existence results on quasilinear equations with convection term and the p-Laplace or the (p, q)-Laplace differential operator we refer to the papers of Bai-Gasiński-Papageorgiou [6], De Figueiredo-Girardi-Matzeu [12], Dupaigne-Ghergu-Rădulescu [13], Faraci-MotreanuPuglisi [14], Faria-Miyag”
• Existence of solutions for double phase obstacle problems with multivalued convection term (2020, background): “Next, we recall the notions of pseudomonotonicity and generalized pseudomonotonicity for multivalued operators (see Gasiński-Papageorgiou [13, Definition 1.4.8]).”
• Positive solutions for nonlinear singular elliptic equations of p-Laplacian type with dependence on the gradient (2019, background): “[16], Gasiński and Papageorgiou [18], and the references therein.”
• Positive solutions for nonlinear Neumann problems with singular terms and convection (2020, methodology): “Of the aformentioned works, only Gasinski & Papageorgiou [5] and Papageorgiou, Rădulescu & Repovš [20] go outside the Dirichlet framework and deal with Neumann problems.”