[PDF] Top 20 Strong Unique Continuation for Solutions of a Laplacian Problem

... of p for bounded solutions. For this purpose we assume throughout this section that 1 < p − ≤ p < ∞ and p is Lipschitz continuous. In particular, p is Log-H ¨older continuous. The new feature in the estimate ... See full document

... With the variational techniques, the p(x)-Laplacian problems with subcritical nonlin- earities have been investigated, see [–] etc. However, the existence of solutions for p(x)-Laplacian problems ... See full document

... global continuation theorem, the generalized Picone identity, and a fixed point index theorem for the index ...positive solutions using the global continuation ...of solutions introduced as ... See full document

... exist solutions for the supercritical case or not is in- teresting for ...the problem for r > p ∗ n–p np is more challenging since it should be shown that the Palais-Smale condition is still valid in ... See full document

... After Kov´aˇcik and R´akosn´ ık first discussed the L px Ω spaces and W k,px Ω spaces in 1, a lot of research has been done concerning these kinds of variable exponent spaces, for example, see 2–5 for the properties of ... See full document

... This article is organized as follows. In Section , we introduce the fractional Sobolev spaces and some preliminary results. In Section , in a suitably chosen framework, we verify that the conditions in the abstract ... See full document

... Furthermore Jiu-Su [] applied Morse theory to study the existence of nontrivial solu- tions of p-Laplacian type Dirichlet boundary value problems. Agarwal-Perera [] obtained two positive solutions of ... See full document

... monotone solutions for initial and boundary value ...p-Laplacian problem involving fractional conformable derivatives is yet to be ...of solutions for the following nonlinear fractional ... See full document

... of unique continuation for the solutions for PDEs began at the early of the last ...inverse problem and control theory. The first quantitative result of strong unique contin- ... See full document

... Obviously, F is continuous and strictly decreasing in R. If y is a constant, the results hold, clearly. Assume y is not a constant. Take a = inf t∈[,+∞) y(t), b = sup t∈[,+∞) y(t). It is easy to see that F(a) > , ... See full document

... Staching complexes are formed by the overlap of the planar regions of aromatic molecules. Nonpolar moieties tend to be squeezed out of water by the strong hydrogen bonding interactions of water. This causes some ... See full document

... local solutions to the initial and boun- dary value problem of a class of parabolic system related to the p-Laplacian are stu- ...approximation solutions, with the help of monotone iteration ... See full document

... Then, we conclude k u k≥ λM 3 C k (u, v) k> λ e 0 M 3 C k (u, v) k=k (u, v) k and so, k (u, v) k=k u k + k v k≥k u k>k (u, v) k, which is a contradiction. Therefore the boundary value problem (1)-(2) has no ... See full document

... This paper deals with the existence of infinitely many solutions for a class of impulsive fractional boundary value problems with p-Laplacian. Based on a variant fountain theorem, the existence of infinitely ... See full document

... Second-order differential equations with the p-Laplacian operator arise in modeling some physical and natural phenomena and can occur, for example, in non-Newtonian mechan- ics, nonlinear elasticity, glaciology, ... See full document

... The existence of infinitely many solutions for some elliptic Dirichlet problems has received a great deal of interest in recent years; see, for instance, the papers 16–20. Moreover, very recently, existence ... See full document

... positive solutions for the fourth-order boundary value problem system with p-Laplacian ...positive solutions for the system is showed through the fixed point index theory in cones under some ... See full document

... It is well known that many interesting and complicated problems in nonlinear analy- sis, such as nonlinear programming, optimization, Nash equilibria, saddle points, fixed points, variational inequalities, and ... See full document

... Among the substantial number of works dealing with nonlinear differential equations we mention the boundary value problem (1.1) and (1.2). We emphasize that the nonlinear term f is involved with the first-order ... See full document

... It is quite natural to study fractional differential equation relative to equation. Re- cently, many scholars have paid more attention to the fractional order differential equation boundary value problems with ... See full document