scholarly journals A double phase equation with convection

2021 ◽  
pp. 1-11
Author(s):  
Zhenhai Liu ◽  
Nikolaos Papageorgiou
Keyword(s):  
Bounded Solution ◽  
Phase Problem ◽  
Nonlinear Operators ◽  
Phase Equation ◽  
Double Phase ◽  
Double Phase Problem ◽  
Monotone Type

We consider a double phase problem with a gradient dependent reaction (convection). Using the theory of nonlinear operators of monotone type, we show the existence of a nontrivial, positive, bounded solution.

scholarly journals Solutions for parametric double phase Robin problems

2021 ◽  
Vol 121 (2) ◽  
pp. 159-170 ◽  
Author(s):  
Nikolaos S. Papageorgiou ◽  
Calogero Vetro ◽  
Francesca Vetro
Keyword(s):  
Boundary Condition ◽  
Existence Theorems ◽  
Robin Boundary Condition ◽  
Phase Problem ◽  
Double Phase ◽  
Robin Boundary ◽  
Double Phase Problem

We consider a parametric double phase problem with Robin boundary condition. We prove two existence theorems. In the first the reaction is ( p − 1 )-superlinear and the solutions produced are asymptotically big as λ → 0 + . In the second the conditions on the reaction are essentially local at zero and the solutions produced are asymptotically small as λ → 0 + .

scholarly journals Anisotropic singular double phase Dirichlet problems

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Nikolaos S. Papageorgiou ◽  
Vicenţiu D. Rǎdulescu ◽  
Youpei Zhang
Keyword(s):  
Positive Solutions ◽  
Singular Term ◽  
Independent Interest ◽  
Phase Problem ◽  
Type Result ◽  
Dirichlet Problems ◽  
Double Phase ◽  
Variational Tools ◽  
Superlinear Perturbation ◽  
Double Phase Problem

<p style='text-indent:20px;'>We consider an anisotropic double phase problem with a reaction in which we have the competing effects of a parametric singular term and a superlinear perturbation. We prove a bifurcation-type result describing the changes in the set of positive solutions as the parameter varies on <inline-formula><tex-math id="M1">\begin{document}$ \mathring{\mathbb{R}}_+ = (0, +\infty) $\end{document}</tex-math></inline-formula>. Our approach uses variational tools together with truncation and comparison techniques as well as several general results of independent interest about anisotropic equations, which are proved in the Appendix.</p>

scholarly journals Existence of Solution for Double-Phase Problem with Singular Weights

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Zhi-Yuan Chen ◽  
Bin Ge ◽  
Wen-Shuo Yuan ◽  
Xiao-Feng Cao
Keyword(s):  
Existence Of Solutions ◽  
Existence Of Solution ◽  
Phase Problem ◽  
Double Phase ◽  
Double Phase Problem ◽  
Singular Weights

The aim of this paper is to establish the existence of solutions for singular double-phase problems depending on one parameter. This work improves and complements the existing ones in the literature. There seems to be no results on the existence of solutions for singular double-phase problems.

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