[PDF] Top 20 Existence of Weak Solutions for a Nonlinear Elliptic System

... the existence, uniqueness, stability, and continuity of solution p to the nonlinear equation ...the existence of weak solutions to Problem ... See full document

... the existence of at least three weak solutions for a doubly eigenvalue elliptic systems involving the p-biharmonic equation with Hardy potential of Kirchhoff type with Navier boundary ...the ... See full document

... renormalized solutions to such problems with q =  and F ≡ ; see [] and [] for ...the existence of bounded weak solutions to this type of problems have been studied in [–], assuming that ... See full document

... the existence of weak solutions for problem () at resonance with the higher eigenvalues of problem ...the existence of weak solutions for problem () by using variational ... See full document

... Also, Dai and Zhang [] showed by using the least action principle that (.) has at least one solution if the potential function has subquadratic growth and, by taking advantage of the fountain theorem due to [], that ... See full document

... a nonlinear elliptic equation in which the divergence form operator − div(a(x, ∇ u)) is ...many nonlinear dif- fusion problems, in particular in the mathematical modeling of non-Newtonian fluids (see ... See full document

... where p > , g(u) is a non-monotone singular term, a ∈ L ∞ (), a(x) ≥  for almost ev- ery x ∈ , λ is a nonnegative parameter and h(u) is continuous. They first established a sub-supersolution theorem and then proved, ... See full document

... [r] ... See full document

... the existence of solutions to nonlinear differential problems is very important as well as the application of such results in the physical ...of nonlinear differential ... See full document

... Yucedag, Existence and multiplicity of weak solutions for nonuniformly elliptic equations with nonstandard growth condition, Complex Variables and Elliptic Equations, 57 2012, no.. On a [r] ... See full document

... has deserved special attention in the last decade. It is not homogeneous and this feature turns out to impose some technical difficulties in applying usual elliptic methods for ob- taining the existence and ... See full document

... Oh, YG: Existence of semiclassical bound states of nonlinear Schrödinger equations with potentials of the class (V) 2.. Commun.[r] ... See full document

... Lakshmikantham, Nonlinear Problems in Abstract Cones, Notes and Reports in Mathematics in Science and Engineering, ...Positive Solutions of Operator Equations, Noordhoff, Groningen, ...the existence ... See full document

... It is our purpose in this paper, to prove the existence of a renormalized solution for the problem (1.1) when the source term has the form f − div F with f ∈ L 1 (Ω) and |F | ∈ E M (Ω), in the setting of Orlicz ... See full document

... Abstract. In this paper we study a class of nonvariational elliptic systems, by using the Gidas-Spruck Blow-up method. first, we obtain a priori estimates, and then using Leray-Schauder topological degree theory, ... See full document

... (u,v) is a solution of (2.2) on [0, T]. Since the right-hand side in (2.2) is Lipschitz con- tinuous in (u, v) ∈ [α/2,α] × [ − β, − β/2], the uniqueness follows. Remark 5.2. Notice that u(r) > 0 and v(r) < 0 for r ... See full document

... One of the mechanisms for getting in and out of the cell, we have the diffusion across the lipid bilayer. Since membranes are held together weak forces, certain molecules can slip between the lipids in the bilayer ... See full document

... which contains the flux term J. The flux term J is a vector field that explains a movement of some physical contents u such as temperature, chemical potential, electrostatic potential, or fluid flows. Physical ... See full document

... for nonlinear elliptic systems have received a lot of interest in recent years (see [–]), particularly when the nonlinear term appears as a source in the equa- tion, complemented with Dirichlet ... See full document

... the existence of bounded solutions to the elliptic system −∆ p u = f (u, v) +h 1 in Ω, −∆ q v = g(u, v) + h 2 in Ω, u = v = 0 on ∂Ω, non-necessarily potential ...the existence of a ... See full document