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1.
In this paper we analyze the free boundary for the inhomogeneous obstacle problem with zero obstacle governed by the degenerate operator
2.
The existence of infinitely many solutions of the following Dirichlet problem for p-mean curvature operator:
is considered, where Θ is a bounded domain in R
n
(n>p>1) with smooth boundary ∂Θ. Under some natural conditions together with some conditions weaker than (AR) condition, we prove that the above problem
has infinitely many solutions by a symmetric version of the Mountain Pass Theorem if
.
Supported by the National Natural Science Foundation of China (10171032) and the Guangdong Provincial Natural Science Foundation
(011606). 相似文献
3.
In this paper, we construct the pseudo-gradient vector field in , by which we obtain the positive and negative cones of are both invariant sets of the descent flow of the corresponding functional. Then we use differential equations theory in Banach spaces and dynamics theory to study p-Laplacian boundary value problems with “jumping” nonlinearities at zero or infinity, and get new multiple solutions and sign-changing solutions theorems of p-Laplacian. 相似文献
4.
In this paper, we consider the following Schrödinger-Poisson system
5.
Jacqueline Fleckinger Evans M. Harrell II François de Thélin 《Bulletin des Sciences Mathématiques》2007,131(7):613
It is shown that the fundamental eigenvalue ratio of the p-Laplacian is bounded by a quantity depending only on the dimension N and p. 相似文献
6.
Farid Madani 《Bulletin des Sciences Mathématiques》2008,132(7):575
Let (Mn,g) be a compact riemannian manifold of dimension n?3. Under some assumptions, we prove that there exists a positive function φ solution of the Yamabe equation
7.
In this paper we establish a priori bounds for positive solutions of the equation
8.
In this paper, we consider the Brezis-Nirenberg problem in dimension N?4, in the supercritical case. We prove that if the exponent gets close to and if, simultaneously, the bifurcation parameter tends to zero at the appropriate rate, then there are radial solutions which behave like a superposition of bubbles, namely solutions of the form
9.
Lawrence C. Evans Ovidiu Savin 《Calculus of Variations and Partial Differential Equations》2008,32(3):325-347
We propose a new method for showing C
1, α
regularity for solutions of the infinity Laplacian equation and provide full details of the proof in two dimensions. The
proof for dimensions n ≥ 3 depends upon some conjectured local gradient estimates for solutions of certain transformed PDE.
LCE is supported in part by NSF Grant DMS-0500452. OS was supported in part by the Miller Institute for Basic Research in
Science, Berkeley. 相似文献
10.
Existence of multiple and sign-changing solutions for a problem involving p-Laplacian and jumping nonlinearities are considered via the construction of descent flow in . Sign-changing and multiple solutions are obtained under additional assumption on the nonlinearity. The uniqueness of positive (negative) solution theorem is included too. 相似文献