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Displaying 81 – 100 of 135

On the eigenvalues of an elliptic operator $a (x, H (u))$

Sergio Campanato (1992)

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

Let $Ω$ be a bounded open convex set of class $C^{2}$ . Let $a (x, H (u))$ be a non linear operator satisfying the condition (A) (elliptic) with constants $α$ , $γ$ , $δ$ . We prove that a number $λ \geq 0$ is an eigenvalue for the operator $a (x, H (u))$ if and only if the number $α λ$ is an eigen-value for the operator $Δ u$ . If $λ \geq 0$ , the two systems $a (x, H (u)) = λ u$ and $Δ u = α λ u$ have the same solutions. In particular, also the eventual eigen-values of the operator $a (x, H (u))$ should all be negative. Finally, we obtain a sufficient condition for the existence of solutions $u \in H^{2} \cap H_{0}^{1} (Ω)$ of the system...

On the existence of a component-wise positive radially symmetric solution for a superlinear system.

Zhidkov, P. (2007)

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

On the existence of a generalized solution to a three-dimensional elliptic equation with radiation boundary condition

László Simon, Gisbert Stoyan (2001)

Applications of Mathematics

For a second order elliptic equation with a nonlinear radiation-type boundary condition on the surface of a three-dimensional domain, we prove existence of generalized solutions without explicit conditions (like ${u |}_{Γ} \in L_{5} (Γ)$ ) on the trace of solutions. In the boundary condition, we admit polynomial growth of any fixed degree in the unknown solution, and the heat exchange and emissivity coefficients may vary along the radiating surface. Our generalized solution is contained in a Sobolev space with an exponent...

On the existence of a positive solution of semilinear elliptic equations in unbounded domains

Abbas Bahri, Pierre-Louis Lions (1997)

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

On the existence of infinitely many solutions for a class of semilinear elliptic equations in $R^{N}$

Francesca Alessio, Paolo Caldiroli, Piero Montecchiari (1998)

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

We show, by variational methods, that there exists a set $A$ open and dense in $a \in L^{\infty} (R^{N}) : a \geq 0$ such that if $a \in A$ then the problem $- △ u + u = a (x) {|u|}^{p - 1} u, u \in H^{1} (R^{N})$ , with $p$ subcritical (or more general nonlinearities), admits infinitely many solutions.

On the existence of positive solution for an elliptic equation of Kirchhoff type via Moser iteration method.

Corrêa, Francisco Júlio S.A., Figueiredo, Giovany M. (2006)

Boundary Value Problems [electronic only]

On the existence of positive solutions of semilinear elliptic equations with Dirichlet boundary conditions.

Z.Q. Chen, R.J. Williams, Z. Zhao (1994)

Mathematische Annalen

On the existence of solutions of some non-linear Dirichlet problems

Jan Bęczek (1988)

Annales Polonici Mathematici

On the existence of solutions to a class of $p$ -Laplace elliptic equations.

He, Hui-Mei, Chen, Jian-Qing (2009)

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

On the existence of the solution of Burger's equation for $n \leq 4$ .

Boules, Adel N. (1990)

International Journal of Mathematics and Mathematical Sciences

On the existence of weak solutions for some quasilinear elliptic variational boundary value problems at resonance

Georg Hetzer (1976)

Commentationes Mathematicae Universitatis Carolinae

On the existence of weak solutions of boundary value problems in a diffusion model for an inhomogeneous liquid in regions with moving boundaries

Salvi, Rodolfo (1985/1986)

Portugaliae mathematica

On the exterior Dirichlet problem for $Δ u - u + f (x, u) = 0$

Giovanna Citti (1992)

Rendiconti del Seminario Matematico della Università di Padova

On the Fast Solutions of Nonlinear Elliptic Equations.

W. Hackbusch (1979)

Numerische Mathematik

On the finite element analysis of problems with nonlinear Newton boundary conditions in nonpolygonal domains

Miloslav Feistauer, Karel Najzar, Veronika Sobotíková (2001)

Applications of Mathematics

The paper is concerned with the study of an elliptic boundary value problem with a nonlinear Newton boundary condition considered in a two-dimensional nonpolygonal domain with a curved boundary. The existence and uniqueness of the solution of the continuous problem is a consequence of the monotone operator theory. The main attention is paid to the effect of the basic finite element variational crimes: approximation of the curved boundary by a polygonal one and the evaluation of integrals by numerical...

Currently displaying 81 – 100 of 135

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Displaying 81 – 100 of 135

On the eigenvalues of an elliptic operator $a (x, H (u))$

On the existence of a component-wise positive radially symmetric solution for a superlinear system.

On the existence of a generalized solution to a three-dimensional elliptic equation with radiation boundary condition

On the existence of a positive solution of semilinear elliptic equations in unbounded domains

On the existence of infinitely many solutions for a class of semilinear elliptic equations in $R^{N}$

On the existence of positive solution for an elliptic equation of Kirchhoff type via Moser iteration method.

On the existence of positive solutions of semilinear elliptic equations with Dirichlet boundary conditions.

On the existence of solutions of some non-linear Dirichlet problems

On the existence of solutions to a class of $p$ -Laplace elliptic equations.

On the existence of the solution of Burger's equation for $n \leq 4$ .

On the existence of weak solutions for some quasilinear elliptic variational boundary value problems at resonance

On the existence of weak solutions of boundary value problems in a diffusion model for an inhomogeneous liquid in regions with moving boundaries

On the exterior Dirichlet problem for $Δ u - u + f (x, u) = 0$

On the Fast Solutions of Nonlinear Elliptic Equations.

On the finite element analysis of problems with nonlinear Newton boundary conditions in nonpolygonal domains

On the first eigenvalue of the Steklov eigenvalue problem for the infinity Laplacian.

On the Ginzburg-Landau energy with weight

On the homogenization of some nonlinear problems in perforated domains

On the influence of domain shape on the existence of large solutions of some superlinear problems.

On the Keldyš-Fichera boundary-value problem for degenerate quasilinear elliptic equations.

Currently displaying 81 – 100 of 135