1.
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Separation of branches of O(N−1)-invariant solutions for a semilinear elliptic equation

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 09/2017, Volume 453, Issue 1, pp. 159 - 173

We consider the problem{−Δu+λu=up in Au>0 in Au=0 on ∂A where A is an annulus in RN, N≥2, p∈(1,+∞) and λ∈[0,+∞). Recent results ensure that there exists a...

Nonradial solutions | Bifurcation | Semilinear elliptic equations | MATHEMATICS | MATHEMATICS, APPLIED | ANNULUS | POSITIVE SOLUTIONS | NONLINEARITIES | UNIQUENESS

Nonradial solutions | Bifurcation | Semilinear elliptic equations | MATHEMATICS | MATHEMATICS, APPLIED | ANNULUS | POSITIVE SOLUTIONS | NONLINEARITIES | UNIQUENESS

Journal Article

Communications in Contemporary Mathematics, ISSN 0219-1997, 12/2019, Volume 21, Issue 8, p. 1850080

For variational problems with O ( N ) -symmetry, the existence of several geometrically distinct solutions has been shown by use of group theoretic approach in...

functional spaces | Orthogonal group | transitive action on the sphere | subspaces of fixed points of subgroups | variational problem with symmetry | MATHEMATICS | MATHEMATICS, APPLIED | sub-spaces of fixed points of subgroups | NONRADIAL SOLUTIONS

functional spaces | Orthogonal group | transitive action on the sphere | subspaces of fixed points of subgroups | variational problem with symmetry | MATHEMATICS | MATHEMATICS, APPLIED | sub-spaces of fixed points of subgroups | NONRADIAL SOLUTIONS

Journal Article

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Finite time blow-up of nonradial solutions in an attraction–repulsion chemotaxis system

Nonlinear Analysis: Real World Applications, ISSN 1468-1218, 04/2017, Volume 34, pp. 335 - 342

This paper considers the attraction–repulsion chemotaxis system: ut=Δu−χ∇⋅(u∇v)+ξ∇⋅(u∇w), 0=Δv+αu−βv, 0=Δw+γu−δw, subject to the non-flux boundary condition in...

Nonradial solutions | Keller–Segel system | Chemotaxis | Attraction–repulsion | Blow-up | EXISTENCE | PATTERN-FORMATION | MATHEMATICS, APPLIED | Keller-Segel system | MICROGLIA | Attraction-repulsion | MODELING CHEMOTAXIS | AGGREGATION

Nonradial solutions | Keller–Segel system | Chemotaxis | Attraction–repulsion | Blow-up | EXISTENCE | PATTERN-FORMATION | MATHEMATICS, APPLIED | Keller-Segel system | MICROGLIA | Attraction-repulsion | MODELING CHEMOTAXIS | AGGREGATION

Journal Article

Journal of Mathematical Physics, ISSN 0022-2488, 12/2019, Volume 60, Issue 12, p. 121510

In this paper, we study the following quasilinear Schrödinger equation with a parameter: −Δu+V(x)u−καΔ(|u|2α)|u|2α−2u=|u|p−2u+|u|(2α)2*−2u in RN, where N ≥...

EXISTENCE | SOLITON-SOLUTIONS | ELLIPTIC-EQUATIONS | WAVE SOLUTIONS | PHYSICS, MATHEMATICAL | NONRADIAL SOLUTIONS | Schroedinger equation | Parameters

EXISTENCE | SOLITON-SOLUTIONS | ELLIPTIC-EQUATIONS | WAVE SOLUTIONS | PHYSICS, MATHEMATICAL | NONRADIAL SOLUTIONS | Schroedinger equation | Parameters

Journal Article

NONLINEARITY, ISSN 0951-7715, 12/2019, Volume 32, Issue 12, pp. 4942 - 4966

We study the following nonlinear scalar field equation {-Delta u -f(u) - mu u in R-N, parallel to u parallel to(2)(L2(RN)) = m, u is an element of H-1(R-N)....

SCHRODINGER-EQUATIONS | EXISTENCE | MATHEMATICS, APPLIED | L-2-subcritical case | nonradial solutions | STABILITY | CALCULUS | CONCENTRATION-COMPACTNESS PRINCIPLE | STANDING WAVES | PHYSICS, MATHEMATICAL | nonlinear scalar field equations | SYMMETRY | sign-changing solutions | Mathematics - Analysis of PDEs | Analysis of PDEs | Mathematics

SCHRODINGER-EQUATIONS | EXISTENCE | MATHEMATICS, APPLIED | L-2-subcritical case | nonradial solutions | STABILITY | CALCULUS | CONCENTRATION-COMPACTNESS PRINCIPLE | STANDING WAVES | PHYSICS, MATHEMATICAL | nonlinear scalar field equations | SYMMETRY | sign-changing solutions | Mathematics - Analysis of PDEs | Analysis of PDEs | Mathematics

Journal Article

ADVANCED NONLINEAR STUDIES, ISSN 1536-1365, 11/2019, Volume 19, Issue 4, pp. 757 - 770

We consider the Henon problem {-Delta u = vertical bar x vertical bar(alpha)u(N+2+2 alpha/N-2-epsilon )in B-1, u > 0 in B-1, u = 0 on partial derivative B-1,...

Henon Problem | MATHEMATICS | MATHEMATICS, APPLIED | SEMILINEAR ELLIPTIC-EQUATIONS | POSITIVE SOLUTIONS | Bifurcation | DOMAINS | Nonradial Solutions | SYMMETRY-BREAKING

Henon Problem | MATHEMATICS | MATHEMATICS, APPLIED | SEMILINEAR ELLIPTIC-EQUATIONS | POSITIVE SOLUTIONS | Bifurcation | DOMAINS | Nonradial Solutions | SYMMETRY-BREAKING

Journal Article

Pacific Journal of Mathematics, ISSN 0030-8730, 2017, Volume 287, Issue 2, pp. 439 - 464

We consider a fractional Schrodinger-Poisson system in R-3. Under certain assumptions, we prove that the problem has infinitely many nonradial positive...

Fractional Schrödinger-Poisson system | Nonradial solutions | Infinitely many solutions | EXISTENCE | MATHEMATICS | infinitely many solutions | fractional Schrodinger-Poisson system | nonradial solutions | BOUND-STATES | SPHERES | SIGN-CHANGING SOLUTIONS | MAXWELL | UNIQUENESS

Fractional Schrödinger-Poisson system | Nonradial solutions | Infinitely many solutions | EXISTENCE | MATHEMATICS | infinitely many solutions | fractional Schrodinger-Poisson system | nonradial solutions | BOUND-STATES | SPHERES | SIGN-CHANGING SOLUTIONS | MAXWELL | UNIQUENESS

Journal Article

Applied Mathematics Letters, ISSN 0893-9659, 04/2020, Volume 102, p. 106142

In this paper, we study the Choquard equation −Δu+V(|x|)u=(∫RNF(|y|,u(y))|x−y|μdy)f(|x|,u),u∈H1(RN),where N≥3, 0<μ Radial solution | Variational method | Choquard equation | Nonradial solution | EXISTENCE | MATHEMATICS, APPLIED | GROUND-STATE SOLUTIONS

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 02/2015, Volume 114, pp. 158 - 168

In this paper, we are concerned with the following quasilinear Schrödinger equation−Δu−uΔ(∣u∣2)+V(∣x∣)u=f(∣x∣,u),x∈RN. By using a change of variables, we...

Radial solution | Nonradial solution | Quasilinear Schrödinger equation | Schrödinger equation | Quasilinear | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | MULTIPLE SOLUTIONS | SCALAR FIELD-EQUATIONS | SOLITON-SOLUTIONS | Quasilinear Schrodinger equation | ELLIPTIC-EQUATIONS | Nonlinearity | Schroedinger equation

Radial solution | Nonradial solution | Quasilinear Schrödinger equation | Schrödinger equation | Quasilinear | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | MULTIPLE SOLUTIONS | SCALAR FIELD-EQUATIONS | SOLITON-SOLUTIONS | Quasilinear Schrodinger equation | ELLIPTIC-EQUATIONS | Nonlinearity | Schroedinger equation

Journal Article

Mathematische Annalen, ISSN 0025-5831, 2/2012, Volume 352, Issue 2, pp. 485 - 515

In this paper we consider the problem $$\left\{\begin{array}{ll}-\Delta u=u^{p}\quad {\rm in}\, \Omega_R,\\ u=0 \quad \quad \quad {\rm on}\,...

Mathematics, general | Mathematics | EXISTENCE | TOPOLOGY | MATHEMATICS | SEMILINEAR ELLIPTIC-EQUATIONS | POSITIVE SOLUTIONS | EXPONENT | SMALL HOLES | NONRADIAL SOLUTIONS

Mathematics, general | Mathematics | EXISTENCE | TOPOLOGY | MATHEMATICS | SEMILINEAR ELLIPTIC-EQUATIONS | POSITIVE SOLUTIONS | EXPONENT | SMALL HOLES | NONRADIAL SOLUTIONS

Journal Article

Discrete and Continuous Dynamical Systems- Series A, ISSN 1078-0947, 02/2018, Volume 38, Issue 2, pp. 547 - 561

We study the p-Laplace elliptic equations in the unit ball under the Dirichlet boundary condition. We call u a least energy solution if it is a minimizer of...

P-Laplace equation | Variational method | Least energy solution | Nonradial solution | Positive solution | MATHEMATICS | nonradial solution | MATHEMATICS, APPLIED | positive solution | ASYMPTOTIC PROFILE | p-Laplace equation | variational method | least energy solution | GROWTH | PRINCIPLE | SUPERCRITICAL HENON EQUATION | GROUND-STATES

P-Laplace equation | Variational method | Least energy solution | Nonradial solution | Positive solution | MATHEMATICS | nonradial solution | MATHEMATICS, APPLIED | positive solution | ASYMPTOTIC PROFILE | p-Laplace equation | variational method | least energy solution | GROWTH | PRINCIPLE | SUPERCRITICAL HENON EQUATION | GROUND-STATES

Journal Article

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Multiple positive solutions of the Emden–Fowler equation in hollow thin symmetric domains

Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 3/2015, Volume 52, Issue 3, pp. 681 - 704

In this paper, we study the Emden–Fowler equation in a hollow thin symmetric domain $$\Omega $$ Ω . Let $$H$$ H and $$G$$ G be closed subgroups of the...

Primary 35J20 | Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Analysis | Theoretical, Mathematical and Computational Physics | Mathematics | 35J25 | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | SEMILINEAR ELLIPTIC-EQUATIONS | ANNULAR DOMAINS | PRINCIPLE | NONRADIAL SOLUTIONS | Partial differential equations | Existence theorems | Mathematical analysis | Texts | Orbits | Calculus of variations | Invariants | Subgroups

Primary 35J20 | Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Analysis | Theoretical, Mathematical and Computational Physics | Mathematics | 35J25 | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | SEMILINEAR ELLIPTIC-EQUATIONS | ANNULAR DOMAINS | PRINCIPLE | NONRADIAL SOLUTIONS | Partial differential equations | Existence theorems | Mathematical analysis | Texts | Orbits | Calculus of variations | Invariants | Subgroups

Journal Article

Advanced Nonlinear Studies, ISSN 1536-1365, 2013, Volume 13, Issue 3, pp. 721 - 738

In this paper we study the generalized Henon equation in the unit ball, where the coefficient function may or may not change its sign. We prove that the least...

Variational method | Group invariant solution | Least energy solution | Nonradial positive solution | Hénon equation | RADIAL SOLUTIONS | MATHEMATICS, APPLIED | STATES | Henon equation | ASYMPTOTIC PROFILE | group invariant solution | variational method | EMDEN-FOWLER EQUATION | nonradial positive solution | UNIQUENESS | MATHEMATICS | least energy solution | GROWTH | ELLIPTIC-EQUATIONS

Variational method | Group invariant solution | Least energy solution | Nonradial positive solution | Hénon equation | RADIAL SOLUTIONS | MATHEMATICS, APPLIED | STATES | Henon equation | ASYMPTOTIC PROFILE | group invariant solution | variational method | EMDEN-FOWLER EQUATION | nonradial positive solution | UNIQUENESS | MATHEMATICS | least energy solution | GROWTH | ELLIPTIC-EQUATIONS

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 10/2013, Volume 406, Issue 1, pp. 277 - 286

In this paper, the Emden–Fowler equation is studied in a hollow thin domain which is invariant under the action of a closed subgroup of the orthogonal group....

Variational method | Group invariant solution | Least energy solution | Emden–Fowler equation | Positive solution | Emden-Fowler equation | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | SEMILINEAR ELLIPTIC-EQUATIONS | ANNULAR DOMAINS | HENON EQUATION | POSITIVE NONRADIAL SOLUTIONS | Energy industry

Variational method | Group invariant solution | Least energy solution | Emden–Fowler equation | Positive solution | Emden-Fowler equation | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | SEMILINEAR ELLIPTIC-EQUATIONS | ANNULAR DOMAINS | HENON EQUATION | POSITIVE NONRADIAL SOLUTIONS | Energy industry

Journal Article

Nonlinear Analysis: Real World Applications, ISSN 1468-1218, 02/2020, Volume 51, p. 102933

In this paper, an attraction–repulsion chemotaxis system with p-Laplacian diffusion...

Global existence | Weak solution | Chemotaxis | [formula omitted]-Laplacian | Attraction–repulsion | EXISTENCE | MATHEMATICS, APPLIED | p-Laplacian | STOKES SYSTEM | LARGE-TIME BEHAVIOR | NONLINEAR DIFFUSION | MODEL | NONRADIAL SOLUTIONS | PATTERN-FORMATION | KELLER-SEGEL SYSTEM | SYMMETRY | Attraction-repulsion | BLOW-UP

Global existence | Weak solution | Chemotaxis | [formula omitted]-Laplacian | Attraction–repulsion | EXISTENCE | MATHEMATICS, APPLIED | p-Laplacian | STOKES SYSTEM | LARGE-TIME BEHAVIOR | NONLINEAR DIFFUSION | MODEL | NONRADIAL SOLUTIONS | PATTERN-FORMATION | KELLER-SEGEL SYSTEM | SYMMETRY | Attraction-repulsion | BLOW-UP

Journal Article

Archiv der Mathematik, ISSN 0003-889X, 9/2017, Volume 109, Issue 3, pp. 263 - 272

We establish the multiplicity of positive solutions to a quasilinear Neumann problem in expanding balls and hemispheres with critical exponent in the boundary...

Nonradial solutions | Neumann problem | 35J20 | 35J92 | Mathematics, general | Mathematics | Critical exponent | Symmetric domains | Multi-peaked solutions | EXISTENCE | MATHEMATICS | P-LAPLACIAN | SEMILINEAR ELLIPTIC-EQUATIONS | INEQUALITIES | CONSTANT | PRINCIPLE

Nonradial solutions | Neumann problem | 35J20 | 35J92 | Mathematics, general | Mathematics | Critical exponent | Symmetric domains | Multi-peaked solutions | EXISTENCE | MATHEMATICS | P-LAPLACIAN | SEMILINEAR ELLIPTIC-EQUATIONS | INEQUALITIES | CONSTANT | PRINCIPLE

Journal Article

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, ISSN 1468-1218, 02/2015, Volume 21, pp. 99 - 109

In this paper, we study the following problem {-Delta(p)u + vertical bar u vertical bar(p-2)u = alpha(x)f(u), x is an element of R-N, u is an element of...

EXISTENCE | MATHEMATICS, APPLIED | p-Laplacian | Nonhomogeneous | Mountain Pass Theorem | EQUATIONS | Cerami sequences | COMPACTNESS | NONRADIAL SOLUTIONS

EXISTENCE | MATHEMATICS, APPLIED | p-Laplacian | Nonhomogeneous | Mountain Pass Theorem | EQUATIONS | Cerami sequences | COMPACTNESS | NONRADIAL SOLUTIONS

Journal Article

Pacific Journal of Mathematics, ISSN 0030-8730, 2016, Volume 284, Issue 2, pp. 395 - 430

We develop a gluing method for fourth-order ODEs and construct infinitely many nonradial singular solutions for a biharmonic equation with supercritical...

Nonradial solutions | Gluing method | Biharmonic supercritical equations | nonradial solutions | ENTIRE RADIAL SOLUTIONS | NONLINEARITY | POSITIVE SOLUTIONS | STABILITY | CLASSIFICATION | LANE-EMDEN EQUATION | MATHEMATICS | biharmonic supercritical equations | R-N | gluing method | ASYMPTOTICS | ELLIPTIC-EQUATIONS

Nonradial solutions | Gluing method | Biharmonic supercritical equations | nonradial solutions | ENTIRE RADIAL SOLUTIONS | NONLINEARITY | POSITIVE SOLUTIONS | STABILITY | CLASSIFICATION | LANE-EMDEN EQUATION | MATHEMATICS | biharmonic supercritical equations | R-N | gluing method | ASYMPTOTICS | ELLIPTIC-EQUATIONS

Journal Article

Mathematische Nachrichten, ISSN 0025-584X, 02/2016, Volume 289, Issue 2-3, pp. 290 - 299

In this paper we study the p‐Laplace Emden–Fowler equation with a radial and sign‐changing weight in the unit ball under the Dirichlet boundary condition. We...

35J20 | positive nonradial solution | 35J25 | Emden–Fowler equation | variational method | least energy solution

35J20 | positive nonradial solution | 35J25 | Emden–Fowler equation | variational method | least energy solution

Journal Article

JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, ISSN 1435-9855, 2012, Volume 14, Issue 6, pp. 1923 - 1953

We address the problem of the existence of finite energy solitary waves for nonlinear Klein-Gordon or Schrodinger type equations Delta u - u + f (u) = 0 in...

EXISTENCE | MATHEMATICS | RADIAL SOLUTIONS | MATHEMATICS, APPLIED | R-N | SCALAR FIELD-EQUATIONS | Lyapunov-Schmidt reduction method | nonlinear Schrodinger equations | NEUMANN PROBLEM | Nonradial bound states | balancing condition | MEAN-CURVATURE SURFACES

EXISTENCE | MATHEMATICS | RADIAL SOLUTIONS | MATHEMATICS, APPLIED | R-N | SCALAR FIELD-EQUATIONS | Lyapunov-Schmidt reduction method | nonlinear Schrodinger equations | NEUMANN PROBLEM | Nonradial bound states | balancing condition | MEAN-CURVATURE SURFACES

Journal Article

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