Results 71 to 80 of about 232 (187)
Karpatsʹkì Matematičnì Publìkacìï, 2018 A homogeneous Dirichlet problem for a semilinear elliptic equations with the Laplace operator and Helmholtz operator is investigated. To construct the two-sided approximations to a positive solution of this boundary value problem the transition to an ...
M.V. Sidorov
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Classification of positive solutions of semilinear elliptic equations
Comptes Rendus. Mathématique, 2003 We give a classification of all solutions of a general semilinear PDE in the positive quadrant of ℝ 2 .
Busca, J, Efendiev, M, Zelik, S
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Entire solutions of semilinear elliptic equations
Electronic Journal of Differential Equations, 2004 We consider existence of entire solutions of a semilinear elliptic equation $Delta u= k(x) f(u)$ for $x in mathbb{R}^n$, $nge3$. Conditions of the existence of entire solutions have been obtained by different authors.
Alexander Gladkov, Nickolai Slepchenkov
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New multiple positive solutions for elliptic equations with singularity and critical growth
Electronic Journal of Qualitative Theory of Differential Equations, 2019 In this note, the existence of multiple positive solutions is established for a semilinear elliptic equation $ -\Delta u=\frac{\lambda}{u^\gamma}+u^{2^*-1},~x\in\Omega,~u=0, x\in\partial\Omega$, where $\Omega$ is a smooth bounded domain in $\mathbb{R}^N$
Hongmin Suo, Chunyu Lei, Jia-Feng Liao
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The Topological State Derivative: An Optimal Control Perspective on Topology Optimisation. [PDF]
J Geom Anal, 2023 Baumann P, Mazari-Fouquer I, Sturm K.
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Multiplicity of Nontrivial Solutions of Semilinear Elliptic Equations
Journal of Mathematical Analysis and Applications, 2000 It is considered the following problem: \(-\Delta u = f(x,u)\) in \(\Omega\), \(u=0\) on \(\partial\Omega\), where \(f\) is a subcritical Carathéodory function. It is proved the existence of at least two nontrivial solutions. This paper unifies and generalizes some results from \textit{A. Castro} and \textit{A. C. Lazer} [Ann. Mat. Pura Appl., IV. Ser.
Liu, Shui-Qiang +2 more
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Multiplicity of solutions for elliptic boundary value problems
Electronic Journal of Differential Equations, 2014 In this article, we study the existence of infinitely many solutions for the semilinear elliptic equation $-\Delta u+a(x)u=f(x,u)$ in a bounded domain of $\mathbb{R}^N$ $(N\geq 3)$ with the Dirichlet boundary conditions, where the primitive of the ...
Yiwei Ye
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A singular perturbation result for a class of periodic-parabolic BVPs
Open MathematicsIn this article, we obtain a very sharp version of some singular perturbation results going back to Dancer and Hess [Behaviour of a semilinear periodic-parabolic problem when a parameter is small, Lecture Notes in Mathematics, Vol. 1450, Springer-Verlag,
Cano-Casanova Santiago +2 more
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Nonexistence results for solutions of semilinear elliptic equations
Duke Mathematical Journal, 1994 Consider the semilinear elliptic equation (1) \(\Delta u= f(| x|)u+ g(x) u^ q\), \(x\in \mathbb{R}_ 0^ N\) for \(N\geq 3\), \(q>1\), where \(\mathbb{R}_ 0^ N= \mathbb{R}^ N\setminus \{0\}\), \(f\in L^ 1_{\text{loc}} (\mathbb{R}_ 0^ +)\), \(g\in L^ \infty_{\text{loc}} (\mathbb{R}_ 0^ N)\), \(g\geq 0\). The main theorems are sufficient conditions on \(f\)
BENGURIA, RD, LORCA, S, YARUR, CS
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Existence of positive solutions for Dirichlet problems of some singular elliptic equations
Electronic Journal of Differential Equations, 2003 When an unbounded domain is inside a slab, existence of a positive solution is proved for the Dirichlet problem of a class of semilinear elliptic equations similar to the singular Emden-Fowler equation.
Zhiren Jin
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