scholarly journals Positive solutions for parametric Dirichlet problems with indefinite potential and superdiffusive reaction

2016 ◽  
pp. 1 ◽  
Author(s):  
Sergiu Aizicovici ◽  
Nikolaos S. Papageorgiou ◽  
Vasile Staicu
Keyword(s):  
Positive Solutions ◽  
Dirichlet Problems ◽  
Indefinite Potential ◽  
Superdiffusive Reaction

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 Positive solutions for a class of singular Dirichlet problems

2019 ◽  
Vol 267 (11) ◽  
pp. 6539-6554 ◽  
Author(s):  
Nikolaos S. Papageorgiou ◽  
Vicenţiu D. Rădulescu ◽  
Dušan D. Repovš
Keyword(s):  
Positive Solutions ◽  
Dirichlet Problems

scholarly journals Multiple Solutions for Partial Discrete Dirichlet Problems Involving the p-Laplacian

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 2030
Author(s):  
Sijia Du ◽  
Zhan Zhou
Keyword(s):  
Positive Solutions ◽  
Dirichlet Boundary ◽  
Nonlinear Term ◽  
Point Theory ◽  
Infinitely Many Solutions ◽  
Discrete Variables ◽  
Dirichlet Problems ◽  
Partial Difference Equations ◽  
Partial Difference ◽  
The Maximum Principle

Due to the applications in many fields, there is great interest in studying partial difference equations involving functions with two or more discrete variables. In this paper, we deal with the existence of infinitely many solutions for a partial discrete Dirichlet boundary value problem with the p-Laplacian by using critical point theory. Moreover, under appropriate assumptions on the nonlinear term, we determine open intervals of the parameter such that at least two positive solutions and an unbounded sequence of positive solutions are obtained by using the maximum principle. We also show two examples to illustrate our results.

scholarly journals Positive solutions for nonlinear parametric singular Dirichlet problems

2018 ◽  
Author(s):  
Nikolaos S. Papageorgiou ◽  
Vicenţiu D. Rădulescu ◽  
Dušan D. Repovš
Keyword(s):  
Positive Solutions ◽  
Dirichlet Problems

On a class of two-dimensional singular elliptic problems

2001 ◽  
Vol 131 (3) ◽  
pp. 479-497 ◽  
Author(s):  
Paolo Caldiroli ◽  
Roberta Musina
Keyword(s):  
Positive Solutions ◽  
Exterior Domain ◽  
Elliptic Problems ◽  
Two Dimensional ◽  
Dirichlet Problems ◽  
Existence Of Positive Solutions

We consider Dirichlet problems of the form −|x|αΔu = λu + g(u) in Ω, u = 0 on ∂Ω, where α, λ ∈ R, g ∈ C(R) is a superlinear and subcritical function, and Ω is a domain in R2. We study the existence of positive solutions with respect to the values of the parameters α and λ, and according that 0 ∈ Ω or 0 ∈ ∂Ω, and that Ω is an exterior domain or not.

Sign in / Sign up

Export Citation Format

Share Document