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We consider three types of semilinear second order PDEs on a cylindrical domain $Ω \times (0, \infty)$ , where $Ω$ is a bounded domain in $ℝ^{N}$ , $N \geq 2$ . Among these, two are evolution problems of parabolic and hyperbolic types, in which the unbounded direction of $Ω \times (0, \infty)$ is reserved for time $t$ , the third type is an elliptic equation with a singled out unbounded variable $t$ . We discuss the asymptotic behavior, as $t \to \infty$ , of solutions which are defined and bounded on $Ω \times (0, \infty)$ .

Some constancy results for harmonic maps from non-contractable domains into spheres.

Zhang, Kewei (2000)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Some constancy results for nematic liquid crystals and harmonic maps

Kai Seng Chou, Xi-Ping Zhu (1995)

Annales de l'I.H.P. Analyse non linéaire

Some critical point theorems and applications to semilinear elliptic partial differential equations

Paul H. Rabinowitz (1978)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Some estimates of solutions to Monge-Ampère type equations in dimension two

Giorgio Talenti (1981)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Some existence results for the scalar curvature problem via Morse theory

Andrea Malchiodi (1999)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We prove existence of positive solutions for the equation $- △_{g_{0}} u + u = (1 + ϵ K (x)) u^{2^{*} - 1}$ on $S^{n}$ , arising in the prescribed scalar curvature problem. is the Laplace-Beltrami operator on $S^{n}$ , $2^{*}$ is the critical Sobolev exponent, and $ϵ$ is a small parameter. The problem can be reduced to a finite dimensional study which is performed with Morse theory.

Some Liouville theorems for the $p$ -Laplacian.

Birindelli, Isabeau, Demengel, Françoise (2002)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Some maximum principles for solutions of a class of partial differential equations in $Ω \subset ℝ^{n}$ .

Al-Mahameed, Mohammad Mujalli (2000)

International Journal of Mathematics and Mathematical Sciences

Some new oscillation criteria for second order elliptic equations with damping

Rong-Kun Zhuang, Zheng-an Yao (2005)

Annales Polonici Mathematici

Some new oscillation criteria are obtained for second order elliptic differential equations with damping $\sum_{i, j = 1}^{n} D_{i} [A_{i j} (x) D_{j} y] + \sum_{i = 1}^{n} b_{i} (x) D_{i} y + q (x) f (y) = 0$ , x ∈ Ω, where Ω is an exterior domain in ℝⁿ. These criteria are different from most known ones in the sense that they are based on the information only on a sequence of subdomains of Ω ⊂ ℝⁿ, rather than on the whole exterior domain Ω. Our results are more natural in view of the Sturm Separation Theorem.

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Displaying 41 – 60 of 129

Solvability of nonlinear Dirichlet problem for a class of degenerate elliptic equations.

Solvability of quasilinear elliptic equations with strong dependence on the gradient.

Solvability of semilinear equations with strong nonlinearities and applications to elliptic boundary value problems

Solving $p$ -Laplacian equations on complete manifolds.

Some approximation properties in Orlicz-Sobolev spaces

Some asymptotic error estimates for finite element approximation of minimal surfaces

Some asymptotic problems in fully nonlinear elliptic equations and stochastic control

Some common asymptotic properties of semilinear parabolic, hyperbolic and elliptic equations