Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2010 The basic boundary value problems for semilinear equations of elliptic type with a spectral parameter and discontinuous nonlinearity are considered in a bounded domain with a sufficiently smooth boundary.
Dmitrij К Potapov
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Infinitely many sign-changing solutions for a semilinear elliptic equation with variable exponent
AIMS Mathematics, 2021 This paper is devoted to study a class of semilinear elliptic equations with variable exponent. By means of perturbation technique, variational methods and a priori estimation, the existence of infinitely many sign-changing solutions to this class of ...
Changmu Chu, Yuxia Xiao , Yanling Xie
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The Free Boundary of a Semilinear Elliptic Equation [PDF]
Transactions of the American Mathematical Society, 1984 The Dirichlet problem Δ u = λ f ( u ) \Delta u = \lambda \,f(u) in a domain Ω , u = 1 \Omega ,\,u = 1 on ∂ Ω \partial \Omega is considered with f ( t
Friedman, Avner, Phillips, Daniel
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Local minimizers in spaces of symmetric functions and applications [PDF]
, 2014 We study $H^1$ versus $C^1$ local minimizers for functionals defined on spaces of symmetric functions, namely functions that are invariant by the action of some subgroups of $\mathcal{O}(N)$.
Dos Santos +3 more
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Partial data inverse problems for semilinear elliptic equations with gradient nonlinearities [PDF]
Mathematical Research Letters, 2019 We show that the linear span of the set of scalar products of gradients of harmonic functions on a bounded smooth domain $\Omega\subset \mathbb{R}^n$ which vanish on a closed proper subset of the boundary is dense in $L^1(\Omega)$.
Katya Krupchyk, G. Uhlmann
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Classification and Liouville-type theorems for semilinear elliptic equations in unbounded domains [PDF]
Analysis & PDE, 2019 We classify stable and finite Morse index solutions to general semilinear elliptic equations posed in Euclidean space of dimension at most 10, or in some unbounded domains.
L. Dupaigne, A. Farina
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Semilinear elliptic equations and fixed points [PDF]
Proceedings of the American Mathematical Society, 2004 In this paper, we deal with a class of semilinear elliptic equation in a bounded domain $ \subset\mathbb{R}^N$, $N\geq 3$, with $C\sp{1,1}$ boundary. Using a new fixed point result of the Krasnoselskii's type for the sum of two operators, an existence principle of strong solutions is proved. We give two examples where the nonlinearity can be critical.
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On the existence of multiple positive entire solutions for a class of quasilinear elliptic equations
International Journal of Mathematics and Mathematical Sciences, 2006 Our goal is to establish the theorems of existence and multiple of positive entire solutions for a class quasilinear elliptic equations in ℝN with the Schauder-Tychonoff fixed point theorem as the principal tool.
Yang Zuodong
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A new proof of the boundedness results for stable solutions to semilinear elliptic equations [PDF]
Discrete and Continuous Dynamical Systems. Series A, 2019 We consider the class of stable solutions to semilinear equations $-\Delta u=f(u)$ in a bounded smooth domain of $\mathbb{R}^n$. Since 2010 an interior a priori $L^\infty$ bound for stable solutions is known to hold in dimensions $n \leq 4$ for all $C^1$
X. Cabré
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On the exact multiplicity of stable ground states of non-Lipschitz semilinear elliptic equations for some classes of starshaped sets [PDF]
Advances in Nonlinear Analysis, 2018 We prove the exact multiplicity of flat and compact support stable solutions of an autonomous non-Lipschitz semilinear elliptic equation of eigenvalue type according to the dimension N and the two exponents, 0 < α < β < 1, of the involved nonlinearites ...
J. Díaz +2 more
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