2016, Graduate studies in mathematics, ISBN 9781470426071, Volume 171., viii, 368

Differential equations, Elliptic | Boundary value problems for second-order elliptic equations | Partial differential equations | Differential equations, Nonlinear | Elliptic equations and systems | Quasilinear elliptic equations with mean curvature operator | Elliptic Monge-Ampère equations | Nonlinear elliptic equations

Book

Nonlinear Analysis, ISSN 0362-546X, 04/2019, Volume 181, pp. 147 - 179

We consider quasilinear elliptic 2m-order (m⩾2) partial differential equations whose prototype is...

Harnack inequality | Quasilinear high-order elliptic equation | Wolff potential | [formula omitted] - [formula omitted] growth | Lorentz space | Zygmund space | m - (p,q) growth | EXISTENCE | LOCAL BEHAVIOR | MATHEMATICS, APPLIED | HOLDER CONTINUITY | Quasilinear high-order elliptice equation m - (p, q) growth | ISOLATED SINGULARITIES | THEOREM | MINIMIZERS | MATHEMATICS | INTEGRAL FUNCTIONALS | REGULARITY | BOUNDARY | GENERALIZED SOLUTIONS | Differential equations | Partial differential equations | Mathematical analysis | Elliptic functions

Harnack inequality | Quasilinear high-order elliptic equation | Wolff potential | [formula omitted] - [formula omitted] growth | Lorentz space | Zygmund space | m - (p,q) growth | EXISTENCE | LOCAL BEHAVIOR | MATHEMATICS, APPLIED | HOLDER CONTINUITY | Quasilinear high-order elliptice equation m - (p, q) growth | ISOLATED SINGULARITIES | THEOREM | MINIMIZERS | MATHEMATICS | INTEGRAL FUNCTIONALS | REGULARITY | BOUNDARY | GENERALIZED SOLUTIONS | Differential equations | Partial differential equations | Mathematical analysis | Elliptic functions

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 08/2019, Volume 185, pp. 206 - 215

We prove an existence result for a quasilinear elliptic equation satisfying natural growth conditions. As a consequence, we deduce an existence result for a...

Quasilinear elliptic equations | Natural growth conditions | Divergence form | Equations with singular drift | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | Mathematical analysis | Drift | Elliptic functions | Mathematics - Analysis of PDEs

Quasilinear elliptic equations | Natural growth conditions | Divergence form | Equations with singular drift | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | Mathematical analysis | Drift | Elliptic functions | Mathematics - Analysis of PDEs

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 11/2012, Volume 395, Issue 1, pp. 78 - 85

We are concerned with the asymptotic analysis of positive blow-up boundary solutions for a class of quasilinear elliptic equations with an absorption term. By...

Boundary blow-up | Quasilinear elliptic equation | Asymptotic analysis | Regular variation theory | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | BIEBERBACH | BEHAVIOR | RADEMACHER | UNIQUENESS

Boundary blow-up | Quasilinear elliptic equation | Asymptotic analysis | Regular variation theory | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | BIEBERBACH | BEHAVIOR | RADEMACHER | UNIQUENESS

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 04/2019, Volume 472, Issue 1, pp. 705 - 727

The paper focuses on a class of supercritical quasilinear Schrödinger elliptic equations−Δu+V(x)u+Δ(u2)u=λf(u),x∈RN, where N≥3. We suppose that the...

Supercritical growth | Quasilinear Schrödinger equations | [formula omitted]-estimate | Variational methods | estimate | MATHEMATICS | MATHEMATICS, APPLIED | L-infinity-estimate | SOLITON-SOLUTIONS | MULTIPLICITY | Quasilinear Schrodinger equations

Supercritical growth | Quasilinear Schrödinger equations | [formula omitted]-estimate | Variational methods | estimate | MATHEMATICS | MATHEMATICS, APPLIED | L-infinity-estimate | SOLITON-SOLUTIONS | MULTIPLICITY | Quasilinear Schrodinger equations

Journal Article

Nonlinear Analysis: Real World Applications, ISSN 1468-1218, 12/2016, Volume 32, pp. 242 - 259

In this paper, under some superquadratic conditions made on the nonlinearity f, we use variational approaches to establish the existence of infinitely many...

Infinitely many solutions | Soliton solution | Quasilinear Schrödinger equation | ([formula omitted])-Laplacian | (p,q)-Laplacian | REACTION-DIFFUSION EQUATIONS | SCHRODINGER-EQUATIONS | EXISTENCE | MATHEMATICS, APPLIED | (p, q)-Laplacian | SOLITON-SOLUTIONS | POSITIVE SOLUTIONS | Quasilinear Schrodinger equation | Q-LAPLACIAN

Infinitely many solutions | Soliton solution | Quasilinear Schrödinger equation | ([formula omitted])-Laplacian | (p,q)-Laplacian | REACTION-DIFFUSION EQUATIONS | SCHRODINGER-EQUATIONS | EXISTENCE | MATHEMATICS, APPLIED | (p, q)-Laplacian | SOLITON-SOLUTIONS | POSITIVE SOLUTIONS | Quasilinear Schrodinger equation | Q-LAPLACIAN

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 01/2013, Volume 254, Issue 1, pp. 102 - 124

We consider a class of quasilinear Schrödinger equations which include the Modified Nonlinear Schrödinger Equations. A new perturbation approach is used to...

Perturbation methods | Quasilinear elliptic equations | Critical exponent

Perturbation methods | Quasilinear elliptic equations | Critical exponent

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 02/2017, Volume 272, Issue 4, pp. 1524 - 1552

In this paper we obtain the following local Calderón–Zygmund estimatesB(|f|)∈Llocq(Ω)⇒B(|∇u|)∈Llocq(Ω)for any q≥1 of weak solutions for a class of quasilinear...

Calderón–Zygmund | Gradient | Elliptic | Quasilinear | MATHEMATICS | Calderfin-Zygmund | REGULARITY | REIFENBERG DOMAINS | BMO COEFFICIENTS | SYSTEMS

Calderón–Zygmund | Gradient | Elliptic | Quasilinear | MATHEMATICS | Calderfin-Zygmund | REGULARITY | REIFENBERG DOMAINS | BMO COEFFICIENTS | SYSTEMS

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 12/2017, Volume 273, Issue 11, pp. 3426 - 3462

The existence of solutions to a class of quasilinear elliptic problems on noncompact Riemannian manifolds, with finite volume, is investigated. Boundary value...

Noncompact manifolds | Quasilinear elliptic equations | Sobolev embeddings | Neumann problems | LAPLACIAN | MATHEMATICS | SPACES | ISOPERIMETRIC-INEQUALITIES | Iron oxides | Analysis | Differential equations | Quasilinear elliptic equations; Sobolev embeddings; Noncompact manifolds; Neumann problems | Naturvetenskap | Matematisk analys | Mathematics | Natural Sciences | Matematik | Mathematical Analysis

Noncompact manifolds | Quasilinear elliptic equations | Sobolev embeddings | Neumann problems | LAPLACIAN | MATHEMATICS | SPACES | ISOPERIMETRIC-INEQUALITIES | Iron oxides | Analysis | Differential equations | Quasilinear elliptic equations; Sobolev embeddings; Noncompact manifolds; Neumann problems | Naturvetenskap | Matematisk analys | Mathematics | Natural Sciences | Matematik | Mathematical Analysis

Journal Article

INDIANA UNIVERSITY MATHEMATICS JOURNAL, ISSN 0022-2518, 2018, Volume 67, Issue 6, pp. 2199 - 2224

This paper is devoted to the study, with variational technique, of the following quasilinear elliptic problem: {-Delta(p)u - beta Delta(q)u = g(u) in R-N, u(x)...

MOUNTAIN PASS | EXISTENCE | MATHEMATICS | R-N | SCALAR FIELD-EQUATIONS | SYMMETRY | SUPERLINEAR (P | variational method | ground state solution | REGULARITY | Quasilinear elliptic equation | Q)-LAPLACIAN

MOUNTAIN PASS | EXISTENCE | MATHEMATICS | R-N | SCALAR FIELD-EQUATIONS | SYMMETRY | SUPERLINEAR (P | variational method | ground state solution | REGULARITY | Quasilinear elliptic equation | Q)-LAPLACIAN

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 05/2017, Volume 155, pp. 97 - 114

In this article we study quasilinear equations model of which are −∑i=1n(|uxi|pi−2uxi)xi+f(u)=0,u≥0,∂u∂t−∑i=1n(u(mi−1)(pi−1)|uxi|pi−2uxi)xi+f(u)=0,u≥0. Despite...

Harnack inequality | Large solutions | A priori estimates | Quasilinear elliptic and parabolic equations | COMPARISON-THEOREMS | MATHEMATICS | MATHEMATICS, APPLIED | SINGULARITIES | STRONG MAXIMUM PRINCIPLE | Analysis | Equality

Harnack inequality | Large solutions | A priori estimates | Quasilinear elliptic and parabolic equations | COMPARISON-THEOREMS | MATHEMATICS | MATHEMATICS, APPLIED | SINGULARITIES | STRONG MAXIMUM PRINCIPLE | Analysis | Equality

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 12/2016, Volume 147, pp. 176 - 190

We deal with the Dirichlet problem for general quasilinear elliptic equations over Reifenberg flat domains. The principal part of the operator supports natural...

Quasilinear elliptic operator | Controlled growths | Small BMO | Weak solution | Regularity | Morrey space | Reifenberg flat domain | MATHEMATICS | MATHEMATICS, APPLIED | CONTINUITY | SYSTEMS

Quasilinear elliptic operator | Controlled growths | Small BMO | Weak solution | Regularity | Morrey space | Reifenberg flat domain | MATHEMATICS | MATHEMATICS, APPLIED | CONTINUITY | SYSTEMS

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 01/2018, Volume 457, Issue 1, pp. 551 - 567

In this paper we obtain the following global Calderón–Zygmund estimatesB(|f|)∈Lq(Ω)⇒B(|∇u|)∈Lq(Ω)for any q≥1 in a convex domain Ω of the weak solution for a...

Calderón–Zygmund | Gradient | Elliptic | p-Laplace | Regularity | Quasilinear | MATHEMATICS | MATHEMATICS, APPLIED | Calderon-Zygmund | BMO COEFFICIENTS

Calderón–Zygmund | Gradient | Elliptic | p-Laplace | Regularity | Quasilinear | MATHEMATICS | MATHEMATICS, APPLIED | Calderon-Zygmund | BMO COEFFICIENTS

Journal Article

Archiv der Mathematik, ISSN 0003-889X, 1/2017, Volume 108, Issue 1, pp. 71 - 83

We study the solution $${u(r,\rho)}$$ u ( r , ρ ) of the quasilinear elliptic problem $$\begin{cases}...

Secondary 35C10 | Singular solutions | Intersection number | 35B32 | Mathematics, general | Mathematics | 70K05 | Quasilinear elliptic equation | Radial solutions | Primary 35B05 | MATHEMATICS

Secondary 35C10 | Singular solutions | Intersection number | 35B32 | Mathematics, general | Mathematics | 70K05 | Quasilinear elliptic equation | Radial solutions | Primary 35B05 | MATHEMATICS

Journal Article

15.
Full Text
Pointwise estimates of Brezis–Kamin type for solutions of sublinear elliptic equations

Nonlinear Analysis, ISSN 0362-546X, 11/2016, Volume 146, pp. 1 - 19

We study quasilinear elliptic equations of the type −Δpu=σuqinRn, where Δpu=∇⋅(∇u|∇u|p−2) is the p-Laplacian (or a more general A-Laplace operator divA(x,∇u)),...

Quasilinear equations | Fractional Laplacian | Wolff potentials | MATHEMATICS | MATHEMATICS, APPLIED | NONLINEAR EQUATIONS | NATURAL GROWTH TERMS | POTENTIAL-THEORY

Quasilinear equations | Fractional Laplacian | Wolff potentials | MATHEMATICS | MATHEMATICS, APPLIED | NONLINEAR EQUATIONS | NATURAL GROWTH TERMS | POTENTIAL-THEORY

Journal Article

Journal of Dynamics and Differential Equations, ISSN 1040-7294, 6/2018, Volume 30, Issue 2, pp. 579 - 600

This study considers the quasilinear elliptic equation with a damping term, $$\begin{aligned} \text {div}(D(u)\nabla u) + \frac{k(|{\mathbf {x}}|)}{|{\mathbf...

Ordinary Differential Equations | 34D23 | 35J92 | Damping term | Quasilinear differential equation | ( $$p, q$$ p , q )-Laplacian | Mathematics | Convergence of solutions | Applications of Mathematics | Partial Differential Equations | Radially symmetric solutions | 34D05 | (p, q)-Laplacian | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | R-N | NONTRIVIAL SOLUTION | Q-LAPLACIAN | Differential equations

Ordinary Differential Equations | 34D23 | 35J92 | Damping term | Quasilinear differential equation | ( $$p, q$$ p , q )-Laplacian | Mathematics | Convergence of solutions | Applications of Mathematics | Partial Differential Equations | Radially symmetric solutions | 34D05 | (p, q)-Laplacian | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | R-N | NONTRIVIAL SOLUTION | Q-LAPLACIAN | Differential equations

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 12/2013, Volume 225, pp. 79 - 91

Picone identities for quasilinear elliptic equations with p(x)-Laplacians are established, and Sturmian comparison theory is developed on the basis of Picone...

Sturmian comparison theorem | Quasilinear elliptic equations | Half-linear elliptic equations | Picone identity | [formula omitted]-Laplacian | Picone-type inequality | p (x) -Laplacian | p(x)-Laplacian | MATHEMATICS, APPLIED | GROWTH | DIFFERENTIAL-EQUATIONS | OPERATORS

Sturmian comparison theorem | Quasilinear elliptic equations | Half-linear elliptic equations | Picone identity | [formula omitted]-Laplacian | Picone-type inequality | p (x) -Laplacian | p(x)-Laplacian | MATHEMATICS, APPLIED | GROWTH | DIFFERENTIAL-EQUATIONS | OPERATORS

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 08/2016, Volume 261, Issue 3, pp. 1796 - 1834

In this paper, we study existence of solutions for the following elliptic problem, related to mean-field games...

Elliptic systems | Mean-field games | Quasilinear elliptic equations | EXISTENCE | MATHEMATICS | NATURAL GROWTH TERMS | Computer entertainment systems

Elliptic systems | Mean-field games | Quasilinear elliptic equations | EXISTENCE | MATHEMATICS | NATURAL GROWTH TERMS | Computer entertainment systems

Journal Article

Advances in Mathematics, ISSN 0001-8708, 01/2013, Volume 232, Issue 1, pp. 513 - 542

We introduce a class of weak solutions to the quasilinear equation −Δpu=σ|u|p−2u in an open set Ω⊂Rn with p>1, where Δpu=∇⋅(|∇u|p−2∇u) is the p-Laplacian...

Elliptic regularity | Quasilinear equations | Weighted integral inequalities | SCHRODINGER OPERATOR | SOURCE TERMS | EXISTENCE | MATHEMATICS | POSITIVE SOLUTIONS | GROWTH | GRADIENT | Naturvetenskap | MATEMATIK | Natural Sciences

Elliptic regularity | Quasilinear equations | Weighted integral inequalities | SCHRODINGER OPERATOR | SOURCE TERMS | EXISTENCE | MATHEMATICS | POSITIVE SOLUTIONS | GROWTH | GRADIENT | Naturvetenskap | MATEMATIK | Natural Sciences

Journal Article

Advances in Nonlinear Analysis, ISSN 2191-9496, 05/2017, Volume 6, Issue 2, pp. 147 - 164

We study Liouville theorems for problems of the form in the framework of Carnot groups. Here is a vector-valued function satisfying Carathéodory condition and...

35J10 | Quasilinear elliptic inequalities | Liouville theorems | 35J62 | 35B45 | 35J70 | 35B53 | 35B51 | 35R03 | Carnot groups | MATHEMATICS | MATHEMATICS, APPLIED | HARNACK INEQUALITY | OPERATORS

35J10 | Quasilinear elliptic inequalities | Liouville theorems | 35J62 | 35B45 | 35J70 | 35B53 | 35B51 | 35R03 | Carnot groups | MATHEMATICS | MATHEMATICS, APPLIED | HARNACK INEQUALITY | OPERATORS

Journal Article

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