Combined effects of singular and exponential nonlinearities in fractional Kirchhoff problems
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This paper establishes the existence of at least two (weak) solutions for the following fractional Kirchhoff problem involving singular and exponential nonlinearities.Abstract:
In this paper we establish the existence of at least two (weak) solutions for the following fractional Kirchhoff problem involving singular and exponential nonlinearities \begin{document}$ \begin{cases} M\left(\|u\|^{{n}/{s}}\right)(-\Delta)^s_{n/s}u = \mu u^{-q}+ u^{r-1}\exp( u^{\beta})\quad\text{in } \Omega,\\ u>0\qquad\text{in } \Omega,\\ u = 0\qquad\text{in } \mathbb R^n \setminus{ \Omega}, \end{cases} $\end{document} where \begin{document}$ \Omega $\end{document} is a smooth bounded domain of \begin{document}$ \mathbb R^n $\end{document} , \begin{document}$ n\geq 1 $\end{document} , \begin{document}$ s\in (0,1) $\end{document} , \begin{document}$ \mu>0 $\end{document} is a real parameter, \begin{document}$ \beta and \begin{document}$ q\in (0,1) $\end{document} .The paper covers the so called degenerate Kirchhoff case andthe existence proofs rely on the Nehari manifold techniques.read more
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Existence of Solutions for a Critical Choquard–Kirchhoff Problem with Variable Exponents
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Discontinuous perturbations of nonhomogeneous strongly-singular Kirchhoff problems
Vicenţiu D. Rădulescu,Vicenţiu D. Rădulescu,Vicenţiu D. Rădulescu,Carlos Alberto Santos,Lais Santos,Marcos L. M. Carvalho +5 more
TL;DR: In this article, the authors considered the Kirchhoff problem in the presence of a strongly-singular term perturbed by a discontinuous nonlinearity of the Heaviside type in the setting of Orlicz-Sobolev space.
References
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TL;DR: In this article, the theory of conjugate convex functions is introduced, and the Hahn-Banach Theorem and the closed graph theorem are discussed, as well as the variations of boundary value problems in one dimension.
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On a dirichlet problem with a singular nonlinearity
TL;DR: In this article, a dirichlet problem with singular nonlinearity is considered, and the authors present a communication in Partial Differential Equations (PDE) approach to solve it.
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On a singular nonlinear elliptic boundary-value problem
Alan C. Lazer,P. J. McKenna +1 more
TL;DR: In this paper, the authors considered the singular boundary value problem with the assumption that p(x) > 0 and certain smoothness assumptions, and showed that there exists a solution which is smooth on Q2 and continuous on Q.
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Sobolev versus Hölder local minimizers and existence of multiple solutions for a singular quasilinear equation
TL;DR: In this paper, the authors employ variational methods in order to show the existence of at least two distinct (positive) solutions of problem (P) in W 1,p 0 ( ).
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Stationary Kirchhoff problems involving a fractional elliptic operator and a critical nonlinearity
TL;DR: In this article, the existence and the asymptotic behavior of non-negative solutions for a class of stationary Kirchhoff problems driven by a fractional integro-differential operator LK and involving a critical nonlinearity were analyzed.