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Eigenvalue problems of quasilinear elliptic systems on Rn.

Gong Bao Li (1987)

Revista Matemática Iberoamericana

In this paper we get the existence results of the nontrivial weak solution (λ,u) of the following eigenvalue problem of quasilinear elliptic systems-Dα (aαβ(x,u) Dβui) + 1/2 Dui aαβ(x,u)Dαuj Dβuj + h(x) ui = λ|u|p-2ui, for x ∈ Rn, 1 ≤ i ≤ N and u = (u1, u2, ..., uN) ∈ E = {v = (v1, v2, ..., vN) | vi ∈ H1(Rn), 1 ≤ i ≤ N},where aαβ(x,u) satisfy the natural growth conditions. It seems that this kind of problem has never been dealt with before.

Eigenvalue questions on some quasilinear elliptic problems

Poulou, M. N., Stavrakakis, N. M. (2007)

Proceedings of Equadiff 11

Eine Bemerkung zur Regularität stationärer Punkte von konform invarianten Variationsintegralen.

Michael Grüter (1986)

Manuscripta mathematica

Energies of $S^{2}$ -valued harmonic maps on polyhedra with tangent boundary conditions

A. Majumdar, J. M. Robbins, M. Zyskin (2008)

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

Erratum: J. Eur. Math. Soc. 1, 237-311 (1999)

Fanghua Lin, Tristan Rivière (2000)

Journal of the European Mathematical Society

Erratum to : “Multiple critical points of perturbed symmetric strongly indefinite functionals”

Denis Bonheure, Miguel Ramos (2009)

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

Everywhere regularity for vectorial functionals with general growth

Elvira Mascolo, Anna Paola Migliorini (2003)

ESAIM: Control, Optimisation and Calculus of Variations

We prove Lipschitz continuity for local minimizers of integral functionals of the Calculus of Variations in the vectorial case, where the energy density depends explicitly on the space variables and has general growth with respect to the gradient. One of the models is $F (u) = \int_{Ω} a (x) {[h (| D u |)]}^{p (x)} d x$ with $h$ a convex function with general growth (also exponential behaviour is allowed).

Everywhere regularity for vectorial functionals with general growth

Elvira Mascolo, Anna Paola Migliorini (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We prove Lipschitz continuity for local minimizers of integral functionals of the Calculus of Variations in the vectorial case, where the energy density depends explicitly on the space variables and has general growth with respect to the gradient. One of the models is $F (u) = \int_{Ω} a (x) {[h (| D u |)]}^{p (x)} d x$ with h a convex function with general growth (also exponential behaviour is allowed).

Existence and asymptotic behaviour of standing waves for quasilinear Schrödinger–Poisson systems in $R^{3}$

Khalid Benmlih, Otared Kavian (2008)

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

Existence and nonexistence of solutions for a quasilinear elliptic system

Qin Li, Zuodong Yang (2015)

Annales Polonici Mathematici

By a sub-super solution argument, we study the existence of positive solutions for the system ⎧ $- Δ_{p} u = a ₁ (x) F ₁ (x, u, v)$ in Ω, ⎪ $- Δ_{q} v = a ₂ (x) F ₂ (x, u, v)$ in Ω, ⎨u,v > 0 in Ω, ⎩u = v = 0 on ∂Ω, where Ω is a bounded domain in $ℝ^{N}$ with smooth boundary or $Ω = ℝ^{N}$ . A nonexistence result is obtained for radially symmetric solutions.

Existence of infinitely many solutions for degenerate and singular elliptic systems with indefinite concave nonlinearities.

Nguyen Thanh Chung (2011)

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

Currently displaying 1 – 20 of 32

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Displaying 1 – 20 of 32

Eigenvalue problems of quasilinear elliptic systems on Rn.

Eigenvalue questions on some quasilinear elliptic problems

Eine Bemerkung zur Regularität stationärer Punkte von konform invarianten Variationsintegralen.

Energies of $S^{2}$ -valued harmonic maps on polyhedra with tangent boundary conditions

Erratum: J. Eur. Math. Soc. 1, 237-311 (1999)

Erratum to : “Multiple critical points of perturbed symmetric strongly indefinite functionals”

Everywhere regularity for vectorial functionals with general growth

Everywhere regularity for vectorial functionals with general growth

Existence and asymptotic behaviour of standing waves for quasilinear Schrödinger–Poisson systems in $R^{3}$

Existence and nonexistence of solutions for a quasilinear elliptic system

Existence and nonexistence results for a class of quasilinear elliptic systems.

Existence and regularity of positive solutions for an elliptic system.

Existence and uniqueness of solutions to a semilinear elliptic system.

Existence of a ray of eigenvalues for equations with discontinuous operators.

Existence of entire positive solutions for a class of semilinear elliptic systems.

Existence of infinitely many solutions for degenerate and singular elliptic systems with indefinite concave nonlinearities.

Existence of least energy solutions to coupled elliptic systems with critical nonlinearities.

Existence of positive solutions for quasilinear elliptic systems involving the $p$ -Laplacian.

Existence of radial positive solutions vanishing at infinity for asymptotically homogeneous systems.

Existence of solutions for a class of elliptic systems in $ℝ^{N}$ involving the p-Laplacian.

Currently displaying 1 – 20 of 32