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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
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
Journal Article
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
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
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
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
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
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
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
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
Journal Article
Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 3/2015, Volume 52, Issue 3, pp. 681 - 704
Journal Article
Advanced Nonlinear Studies, ISSN 1536-1365, 2013, Volume 13, Issue 3, pp. 721 - 738
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
Journal Article
by Li, Yan
Nonlinear Analysis: Real World Applications, ISSN 1468-1218, 02/2020, Volume 51, p. 102933
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
Journal Article
by Ge, B and Zhou, QM and Zu, L
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
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
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
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
Journal Article
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