Elliptic System
Multiplicity result for a critical elliptic system with concave-convex nonlinearities
... The celebrated papers by Brezis and Nirenberg [] and by Ambrosetti et al. [] have inspired research on differential equations and systems with critical terms, and with concave-convex nonlinearities, respectively, see, ...
10
Existence and multiplicity results for a degenerate quasilinear elliptic system near resonance
... We establish existence and multiplicity results for weak solutions of a degenerate quasilinear elliptic system. By using Ekeland’s variational principle, the mountain pass theorem and the saddle point ...
10
Nontrivial solutions for a quasilinear elliptic system
... quasilinear elliptic system, they es- tablish the existence of two opposite constant sign solutions; in the case where the system has a variational structure, under the proper hypotheses, they obtain ...
9
On symmetric solutions of a critical semilinear elliptic system involving the Caffarelli Kohn Nirenberg inequality in \(\mathbb{R}^{N}\)
... singular elliptic systems in [–] and when G = O( N ), several radial and nonradial results for nonsingular elliptic systems in ...singular elliptic system ...
22
Some elliptic system and reduction method
... We get a theorem which shows the existence of at least three solutions for some elliptic system with Dirichlet boundary condition. We obtain this result by using the finite dimensional reduction method for ...
13
Multiple positive solutions for a fractional elliptic system with critical nonlinearities
... In this paper, we study the multiplicity results of positive solutions for a fractional elliptic system involving both concave-convex and critical growth terms. With the help of the Nehari manifold and the ...
18
Steady states of a nonlinear elliptic system arising from population dynamics
... In this paper, we study the existence and multiplicity of coexistence states for an elliptic system modeling two subpopulations of the same species competing for resources. Our results generalize and ...
7
The estimates on the energy functional of an elliptic system with Neumann boundary conditions
... A more direct approach was proposed in [–]. In these papers, the authors extend the idea, which is introduced by Del Pino and Felmer in [], to system (.). In [], Pistoia and Ramos proved the least energy ...
11
The existence of positive solutions to an elliptic system with nonlinear boundary conditions
... 3. de Figueiredo, DG: Semilinear elliptic systems: a survey of superlinear problems. Resenhas 2, 373-391 (1996) 4. de Figueiredo, DG, Felmer, PL: On superquadratic elliptic systems. Trans. Am. Math. Soc. ...
17
The Keller–Osserman-type conditions for the study of a semilinear elliptic system
... reducing system (1.1) to a system of second-order ODEs and giving a complete classification of its ...setting, system (1.1) becomes a system of differential equations of the ...
14
Semi-classical solutions of perturbed elliptic system with general superlinear nonlinearity
... under various hypotheses on the potential V and the nonlinearity g ; for example, see [– ] and references therein. In a very recent paper [], Lin and Tang developed a direct and simple approach to show the ...
13
Fourth order elliptic system with dirichlet boundary condition
... In section 2 we define a Banach space H spanned by eigenfunctions of Δ 2 + c Δ with Dirichlet boundary condition and investigate some properties of system (1.1). In sec- tion 3, we prove Theorem 1.1 by using the ...
9
Existence of solutions for a general quasilinear elliptic system via perturbation method
... solution for equation (.) from the classical results given by Berestycki and Lions []. Liu et al. [] established the existence of both one-sign and nodal ground states of soliton-type solutions for equation (.) by ...
16
Existence and uniqueness of solutions for a semilinear elliptic system
... nonlinear elliptic equations with boundary ...the system reduces to the homogeneous Dirichlet problem for the biharmonic equation ∆ 2 u = | u | p in a ball with p > ...
17
Existence of Weak Solutions for a Nonlinear Elliptic System
... We investigate the existence of weak solutions to the following Dirichlet boundary value problem, which occurs when modeling an injection molding process with a partial slip condition on[r] ...
15
Existence of solutions for perturbed elliptic system with critical exponents
... Oh, YG: Existence of semiclassical bound states of nonlinear Schrödinger equations with potentials of the class (V) 2.. Commun.[r] ...
13
Simplicity and stability of the first eigenvalue of a nonlinear elliptic system
... Note that the system (1.1) is of two second-order elliptic equations. It is weakly coupled in the sense that interaction is present only in the “source terms,” while the di ff eren- tial terms have only one ...
9
Global Existence and Blow Up Solutions and Blow Up Estimates for Some Evolution Systems with p Laplacian with Nonlocal Sources
... The outline of the paper is as follows. In the next section, we investigate the global nonexistence for elliptic system (1.2). Section 3 is devoted to blow-up estimate for sys- tem (1.1). In Section 4, we ...
17
On the solvability conditions of the first boundary value problem for a system of elliptic equations that strongly degenerate at a point
... an elliptic equation with degeneracy at an inner point of the considered domain are obtained in ...degenerating elliptic equation with the main part of Laplace ’ s operator is ...degenerate elliptic ...
11