[PDF] Top 20 Existence of weak solutions for a class of quasilinear elliptic systems

... 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

... the existence and uniqueness of weak solutions for a new class of initial/boundary-value parabolic problems with nonlinear perturbation term in weighted Sobolev ...new class of ... See full document

... Using variational methods, we prove the existence and nonexistence of positive solutions for a class of ( p , q )-Laplacian systems with a parameter.. Copyright © 2007 S.[r] ... See full document

... nonlinearity f in the case of p-Laplacian type were extended to the case of φ-Laplacian type (for example, see [, , ]). However, there are very few results regarding the exis- tence of ground state for equations ... See full document

... The goal of this paper is to study a nonlinear elliptic equation in which the divergence form operator − div(a(x, ∇ u)) is involved. Such operators appear in many nonlinear dif- fusion problems, in particular in ... See full document

... Theorem 2. Assume (A1),(A2),(A3)(or (A3)’),(G) and (E) hold. Then there exist an open interval Λ ⊆ [0, ∞) and a positive real number r with the following property: for each l Î Λ, there exists s > 0 such that for each ... See full document

... Dong, G: An existence theorem for weak solutions for a class of elliptic partial differential systems in general Orlicz-Sobolev spaces.. Fang, X, Yu, J: Solutions to operator equations on[r] ... See full document

... the existence and multiplicity of symmetric solutions for a class of singular quasilinear elliptic systems involving multiple critical Hardy-Sobolev exponents in a bounded ... See full document

... the existence of an interval Λ such that, for each l Î Λ , the system (1) admits a sequence of pairwise distinct weak solutions is proved; (see Theorem ... See full document

... for solutions of elliptic equations and systems has been extensively ...for solutions to linear elliptic equations and systems in divergence form with continuous ...of ... See full document

... the existence of infinitely many solutions for a class of quasilinear elliptic problems involving the p(x)-Laplace type operator with nonlinear boundary conditions without using the ... See full document

... space Weak convergence is a basic tool of modern nonlinear analysis, because it has the same compactness properties as the convergence in finite dimensional spaces (see ... See full document

... (See Lemma 2.3 for the proof of existence.) Let (u, v) be any solution, which exists by hypothesis, to (3.5) with a > h(0) and b = 0. Without loss of gen- erality, we will assume that a ≥ 1. We now show that h ... See full document

... In this case, the equations arise in problems of existence of stationary waves for anisotropic Schrödinger equation (see []) and others problems (for example, see [, ]). We cite [] for p = ; and [, ] ... See full document

... right-hand side of the system which will ensure the mountain pass geometry and Palais- Smale condition for the corresponding Euler-Lagrange functional of the system, the author limits himself to the subcritical case for ... See full document

... is the well-known p-Laplacian equation. There is a large number of papers on the exis- tence of solutions for the p-Laplacian equation. But the problem (.) possesses more com- plicated nonlinearities. For ... See full document

... for weak solutions to quasilinear elliptic systems under a super quadratic controllable growth condition, and we obtain a general criterion for a weak solution to be regular in ... See full document

... 0 < ξ ≤ z(r) ≤ 2ξ ≤ η ≤ y(r) ≤ 2η. (3.50) On the other hand, if the problem (3.9) has a solution y(r), then v(x) = y( | x | ) = y(r) is a solution of (3.7). Similarly, if the initial value problem (3.45) has ... See full document

... where F(t) = 0 t f (s) ds. It is well known that the (AR)-condition is quite natural and im- portant not only to ensure that an Euler–Lagrangian functional has the mountain pass geometry, but also to guarantee that the ... See full document

... the existence of multiple solutions for a quasilinear system in- volving a pair of (p(x), q(x))-Laplacian ...multiple solutions for a class of differential inclusion systems ... See full document