Results 181 to 190 of about 1,290,485 (220)
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On some Semilinear Elliptic Equations
AIP Conference Proceedings, 2009In this paper we study the third type boundary value problem for a Semilinear Elliptic Equation. Here the existence of the weak solution for the considered problem is proved and also the uniqueness of the solution of the considered problem, in a model case, is proved.
Kerime Kalli +4 more
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On a semilinear elliptic equation in Hn
ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE, 2009We prove existence/nonexistence and uniqueness of positive entire solutions for some semilinear elliptic equations on the Hyperbolic space.
Mancini, Gianni, Sandeep, Kunnath
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On the Existence of Positive Solutions of Semilinear Elliptic Equations
SIAM Review, 1982In this paper we study the existence of positive solutions of semilinear elliptic equations. Various possible behaviors of nonlinearity are considered, and in each case nearly optimal multiplicity results are obtained. The results are also interpreted in terms of bifurcation diagrams.
P L Lions
exaly +3 more sources
Nonconvergent radial solutions of semilinear elliptic equations
Asymptotic Analysis, 2010For 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, 2002The singularly perturbed problem for the semilinear elliptic equations is considered. Under appropriate conditions, by using the comparison theorem, the existence and asymptotic behavior of solution for the boundary value problems are studied.
Ge, Hongxia, Ding, Li
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Singular Solutions for some Semilinear Elliptic Equations
Archive for Rational Mechanics and Analysis, 1987This 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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Variational methods and semi-linear elliptic equations
Archive for Rational Mechanics and Analysis, 1986This work is devoted to obtaining non-resonance and resonance conditions for semilinear elliptic equations by means of variational methods.
Mawhin, Jean, Ward, JR., Willem, Michel
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On the Infinitely Many Solutions of a Semilinear Elliptic Equation
SIAM Journal on Mathematical Analysis, 1986A dynamical systems approach is developed for studying the spherically symmetric solutions of $\Delta u + f(u) = 0$, where $f(u)$ grows like $| u |^\sigma u$ as $| u | \to \infty $ . Various scalings are introduced to elucidate the singular behavior near the center and at infinity. The solutions of interest appear as trajectories in a three-dimensional
Jones, C., Küpper, T.
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Approximation of Sparse Controls in Semilinear Elliptic Equations
2012Semilinear 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 +2 more
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Asymptotic Theory of Singular Semilinear Elliptic Equations
Canadian Mathematical Bulletin, 1984AbstractNecessary 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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