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Displaying 141 – 160 of 185

On the number of positive solutions of singularly perturbed 1D nonlinear Schrödinger equations

Patricio Felmer, Salomé Martínez, Kazunaga Tanaka (2006)

Journal of the European Mathematical Society

We study singularly perturbed 1D nonlinear Schrödinger equations (1.1). When $V (x)$ has multiple critical points, (1.1) has a wide variety of positive solutions for small $ε$ and the number of positive solutions increases to $\infty$ as $ε \to 0$ . We give an estimate of the number of positive solutions whose growth order depends on the number of local maxima of $V (x)$ . Envelope functions or equivalently adiabatic profiles of high frequency solutions play an important role in the proof.

On the optimal control of coefficients in elliptic problems. Application to the optimization of the head slider

Ionel Ciuperca, Mohamed El Alaoui Talibi, Mohammed Jai (2005)

ESAIM: Control, Optimisation and Calculus of Variations

We consider an optimal control problem for a class of non-linear elliptic equations. A result of existence and uniqueness of the state equation is proven under weaker hypotheses than in the literature. We also prove the existence of an optimal control. Applications to some lubrication problems and numerical results are given.

On the optimal control of coefficients in elliptic problems. Application to the optimization of the head slider

Ionel Ciuperca, Mohamed El Alaoui Talibi, Mohammed Jai (2010)

ESAIM: Control, Optimisation and Calculus of Variations

On the optimal growth of functions with bounded Laplacian.

Karp, Lavi, Shahgholian, Henrik (2000)

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

On the oscillation of forced second order mixed-nonlinear elliptic equations

Zhiting Xu (2010)

Annales Polonici Mathematici

Oscillation theorems are established for forced second order mixed-nonlinear elliptic differential equations ⎧ ${d i v (A (x) | | \nabla y | |}^{p - 1} {\nabla y) + ⟨ b (x), | | \nabla y | |}^{p - 1} \nabla y ⟩ + C (x, y) = e (x)$ , ⎨ ⎩ $C (x, y) = {c (x) | y |}^{p - 1} y + \sum_{i = 1}^{m} c_{i} (x) {| y |}^{p_{i} - 1} y$ under quite general conditions. These results are extensions of the recent results of Sun and Wong, [J. Math. Anal. Appl. 334 (2007)] and Zheng, Wang and Han [Appl. Math. Lett. 22 (2009)] for forced second order ordinary differential equations with...

On the principal eigenvalue of elliptic operators in $ℝ^{N}$ and applications

Henry Berestycki, Luca Rossi (2006)

Journal of the European Mathematical Society

Two generalizations of the notion of principal eigenvalue for elliptic operators in $ℝ^{N}$ are examined in this paper. We prove several results comparing these two eigenvalues in various settings: general operators in dimension one; self-adjoint operators; and “limit periodic” operators. These results apply to questions of existence and uniqueness for some semilinear problems in the whole space. We also indicate several outstanding open problems and formulate some conjectures.

On the radial solutions of a degenerate quasilinear elliptic equation in $𝐑^{N}$

Betteoui Benyounes, Abdelilah Gmira (1999)

Annales de la Faculté des sciences de Toulouse : Mathématiques

On the radially symmetric solutions of a BVP for a class of nonlinear elliptic partial differential equations.

Hegedűs, Jenő (2000)

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

On the range of nonlinear operators with linear asymptotes which are not invertible

Djairo Guedes de Figueiredo (1974)

Commentationes Mathematicae Universitatis Carolinae

On the regularity of weak solutions to non linear elliptic systems of partial differential equations.

M. Giaquinta, J. Necas (1980)

Journal für die reine und angewandte Mathematik

On the regularity of weak solutions to nonlinear elliptic systems via Liouville's type property

Mariano Giaquinta, Jindřich Nečas (1979)

Commentationes Mathematicae Universitatis Carolinae

On the regularity of weak solutions to nonlinear elliptic systems of partial differential equations [Abstract of thesis]

Josef Daněček (1985)

Commentationes Mathematicae Universitatis Carolinae

On the regularity up to the boundary for higher order quasilinear elliptic systems

Eugen Viszus (1990)

Commentationes Mathematicae Universitatis Carolinae

On the rigidity of minimal mass solutions to the focusing mass-critical NLS for rough initial data.

Li, Dong, Zhang, Xiaoyi (2009)

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

On the sets of regularity of solutions for a class of degenerate nonlinear elliptic fourth-order equations with $L^{1}$ data.

Bonafede, S., Nicolosi, F. (2007)

Boundary Value Problems [electronic only]

On the smoothness of weak solutions of strong-nonlinear nondiagonal elliptic systems (the two-dimensional case).

Arkhipova, A. (2004)

Zapiski Nauchnykh Seminarov POMI

On the solution of a generalized system of von Kármán equations

Jozef Kačur (1981)

Aplikace matematiky

A nonlinear system of equations generalizing von Kármán equations is studied. The existence of a solution is proved and the relation between the solutions of the considered system and the solutions of von Kármán system is studied. The system considered is derived in a former paper by Lepig under the assumption of a nonlinear relation between the intensity of stresses and deformations in the constitutive law.

Currently displaying 141 – 160 of 185

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Displaying 141 – 160 of 185

On the number of positive solutions of singularly perturbed 1D nonlinear Schrödinger equations

On the optimal control of coefficients in elliptic problems. Application to the optimization of the head slider

On the optimal control of coefficients in elliptic problems. Application to the optimization of the head slider

On the optimal growth of functions with bounded Laplacian.

On the oscillation of forced second order mixed-nonlinear elliptic equations

On the principal eigenvalue of elliptic operators in $ℝ^{N}$ and applications

On the radial solutions of a degenerate quasilinear elliptic equation in $𝐑^{N}$

On the radially symmetric solutions of a BVP for a class of nonlinear elliptic partial differential equations.

On the range of nonlinear operators with linear asymptotes which are not invertible

On the regularity of weak solutions to non linear elliptic systems of partial differential equations.

On the regularity of weak solutions to nonlinear elliptic systems via Liouville's type property

On the regularity of weak solutions to nonlinear elliptic systems of partial differential equations [Abstract of thesis]

On the regularity up to the boundary for higher order quasilinear elliptic systems

On the rigidity of minimal mass solutions to the focusing mass-critical NLS for rough initial data.

On the sets of regularity of solutions for a class of degenerate nonlinear elliptic fourth-order equations with $L^{1}$ data.

On the smoothness of weak solutions of strong-nonlinear nondiagonal elliptic systems (the two-dimensional case).

On the solution of a generalized system of von Kármán equations

On the solvability of degenerated quasilinear elliptic problems.

On the solvability of monge-ampere type equations in non-uniformly convex domains.

On the Solvability of Semilinear Elliptic Equations with Nonlinear Boundary Conditions.

Currently displaying 141 – 160 of 185