Results 201 to 210 of about 2,254 (236)

Nonconvergent radial solutions of semilinear elliptic equations

Asymptotic Analysis, 2010
For many known examples of semilinear elliptic equations Δu+f(u)=0 in R N (N>1), a bounded radial solution u(r) converges to a constant as r→∞. Maier, in 1994, constructed, for N=2, an equation with a nonconvergent radial solution.
Man Kam Kwong, Solomon Wai-Him Wong
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A Class of Singularly Perturbed Semilinear Elliptic Equations

Journal of Partial Differential Equations, 2002
A singularly perturbed problem for semilinear elliptic equations in a strip domain in \(\mathbb R^n\) is considered. The existence and asymptotic behaviour of the solution is established under appropriate conditions. A formal solution in the form of power series with respect to the perturbation parameter is, thereafter using a comparison theorem and ...
Ge, Hongxia, Ding, Li
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Singular Solutions for some Semilinear Elliptic Equations

Archive for Rational Mechanics and Analysis, 1987
This paper studies solutions \(u\in C\) \(2(B_ R\setminus 0)\) of the equation \(-\Delta u+u\) \(p=0\), \(u\geq 0\) on \(B_ R\setminus 0\), the dimension of the underlying space being N.
Brézis, Haïm, Oswald, Luc
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On the Infinitely Many Solutions of a Semilinear Elliptic Equation

SIAM Journal on Mathematical Analysis, 1986
Die Autoren untersuchen sphärisch symmetrische Lösungen von \[ (*)\quad \Delta u+f(u)=0\quad im\quad {\mathbb{R}}^ n, \] wobei die Nichtlinearität f die folgenden Bedingungen erfüllt: (1) \(f\in C^ 1\); (2) \(f(u)=k(u)| u|^{\sigma}u+g(u)\) mit \(k(u)=k_+\), \(u\geq 0\); \(k(u)=k_-\), \(u0\), \(k_->0\) \(g(u)=O(| u|^{\gamma})\), \(g'(u)=O(| u|^{\gamma ...
Jones, C., Küpper, T.
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Asymptotic Theory of Singular Semilinear Elliptic Equations

Canadian Mathematical Bulletin, 1984
AbstractNecessary and sufficient conditions are found for the existence of two positive solutions of the semilinear elliptic equation Δu + q(|x|)u = f(x, u) in an exterior domain Ω⊂ℝn, n ≥ 1, where q, f are real-valued and locally Hölder continuous, and f(x, u) is nonincreasing in u for each fixed x∈Ω. An example is the singular stationary Klein-Gordon
Kusano, Takasi, Swanson, Charles A.
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Nontrivial solutions of elliptic semilinear equations¶at resonance

manuscripta mathematica, 2000
The authors consider the following Dirichlet problem \(-\Delta u = \lambda_m +f(x,u)\) in a bounded domain \(\Omega\) with smooth boundary, where \(\lambda _m\) is an eigenvalue of the Laplacian operator in \(\Omega\) with Dirichlet boundary data. They treat the doubly resonant case, both at infinity and zero, \(\lim_{t\to 0}f(x,t)/t= \lim_{t\to \infty}
Perera, Kanishka, Schechter, Martin
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Global Positive Solutions of Semilinear Elliptic Equations

Canadian Journal of Mathematics, 1983
The semilinear elliptic boundary value problem1.1will be considered in an exterior domain Ω ⊂ Rn, n ≥ 2, with boundary ∂Ω ∊ C2 + α, 0 < α < 1, where1.2Di = ∂/∂xi, i = 1, …, n. The coefficients aij, bi in (1.2) are assumed to be real-valued functions defined in Ω ∪ ∂Ω such that each , , and (aij(x)) is uniformly positive definite in every bounded ...
Noussair, Ezzat S., Swanson, Charles A.
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Approximation of Sparse Controls in Semilinear Elliptic Equations

2012
Semilinear elliptic optimal control problems involving the L1 norm of the control in the objective are considered. Necessary and sufficient second-order optimality conditions are derived. A priori finite element error estimates for three different discretizations for the control problem are given.
Eduardo Casas, Roland Herzog, Gerd Wachsmuth   +2 more
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On the iterative and minimizing sequences for semilinear elliptic equations (I)

Japan Journal of Industrial and Applied Mathematics, 1995
Les auteurs continuent leur précédente recherche [ibid. 12, No. 2, 309-326 (1995; Zbl 0842.35004)] sur la solution numérique de l'équation elliptique semilinéaire (1) \(-\Delta u= f(u)\) dans \(\Omega\), avec la condition (2) \(u=0\) sur \(\partial \Omega\), où \(\Omega\) est un domaine polygonal à deux dimension.
Mizutani, Akira, Suzuki, Takashi
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ON THE EXISTENCE OF PERIODIC SOLUTIONS OF SEMILINEAR ELLIPTIC EQUATIONS

Russian Academy of Sciences. Sbornik Mathematics, 1994
Summary: Using a variational method, the existence of a solution of the equation \(-\Delta u=g(u)\) in \(\mathbb{R}^{N+1}\) is proved, periodic with respect to one variable and localized with respect to the remaining variables.
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