A class of functionals possessing multiple global minima [PDF]
, 2022 We get a new multiplicity result for gradient systems. Here is a very particular corollary: Let Ω ⊂ Rn (n ≥ 2) be a smooth bounded domain and let Φ : R2 → R be a C1 function, with Φ(0, 0) = 0, such that... Mathematics Subject Classification (2010): 35J47,
RICCERI, Biagio
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Nonautonomous fractional Hamiltonian system with critical exponential growth [PDF]
, 2019 International audienceIn this paper, we study the following nonlocal nonautonomous Hamiltonian system on whole R (−∆) 1 2 u + u = Q(x)g(v) in R, (−∆) 1 2 v + v = P (x)f (u) in R, where (−∆) 1 2 is the square root Laplacian operator.
Marcos, João +2 more
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A Caccioppoli-type estimate for very weak solutions to obstacle problems with weight [PDF]
, 2011 This paper gives a Caccioppoli-type estimate for very weak solutions to obstacle problems of the A -harmonic equation div A ( x , ∇ u ) = 0 with | A ( x , ξ ) | ≈ w ( x ) | ξ | p - 1 , where 1 < p < ...
Gao Hongya +3 more
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Concentration behavior of semiclassical solutions for Hamiltonian elliptic system
Advances in Nonlinear Analysis, 2020 In this paper, we study the following nonlinear Hamiltonian elliptic system with gradient ...
Zhang Jian +3 more
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Ground states of Schrödinger systems with the Chern-Simons gauge fields
Advanced Nonlinear Studies, 2023 We are concerned with the following coupled nonlinear Schrödinger system: −Δu+u+∫∣x∣∞h(s)su2(s)ds+h2(∣x∣)∣x∣2u=∣u∣2p−2u+b∣v∣p∣u∣p−2u,x∈R2,−Δv+ωv+∫∣x∣∞g(s)sv2(s)ds+g2(∣x∣)∣x∣2v=∣v∣2p−2v+b∣u∣p∣v∣p−2v,x∈R2,\left\{\begin{array}{l}-\Delta u+u+\left(\underset{|
Jiang Yahui +4 more
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Fourth order elliptic system with dirichlet boundary condition [PDF]
, 2011 We investigate the multiplicity of the solutions of the fourth order elliptic system with Dirichlet boundary condition. We get two theorems. One theorem is that the fourth order elliptic system has at least two nontrivial solutions when λ k < c &
Tacksun Jung +3 more
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Stability of solitary-wave solutions of coupled NLS equations with power-type nonlinearities
Advances in Nonlinear Analysis, 2015 This paper proves existence and stability of solitary-wave solutions of a system of 2-coupled nonlinear Schrödinger equations with power-type nonlinearities arising in several models of modern physics. The existence of vector solitary-wave solutions (i.e.
Bhattarai Santosh
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Multiple positive solutions for quasilinear elliptic problems with sign‐changing nonlinearities
Abstract and Applied Analysis, Volume 2004, Issue 12, Page 1047-1055, 2004., 2004 Using variational arguments, we prove some nonexistence and multiplicity results for positive solutions of a system of p‐Laplace equations of gradient form. Then we study a p‐Laplace‐type problem with nonlinear boundary conditions.
Julián Fernández Bonder
wiley +1 more source
A note on the variational structure of an elliptic system involving critical Sobolev exponent
Journal of Applied Mathematics, Volume 2003, Issue 5, Page 227-241, 2003., 2003 We consider an elliptic system involving critical growth conditions. We develop a technique of variational methods for elliptic systems. Using the well‐known results of maximum principle for systems developed by Fleckinger et al. (1995), we can find positive solutions.
Mario Zuluaga
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Quasilinear elliptic systems of resonant type and nonlinear eigenvalue problems
Abstract and Applied Analysis, Volume 7, Issue 3, Page 155-167, 2002., 2002 This work is devoted to the study of a quasilinear elliptic system of resonant type. We prove the existence of infinitely many solutions of a related nonlinear eigenvalue problem. Applying an abstract minimax theorem, we obtain a solution of the quasilinear system −Δpu = Fu(x, u, v), − Δqv = F v(x, u, v), under conditions involving the first and the ...
Pablo L. de Nàpoli, M. Cristina Mariani
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