The singularity may appear at u s 0 and at t s 0 or t s 1 and the function f may be discontinuous. The authors prove that for any p ) 1 and for any positive, nonincreasing function f and nonnegative measurable function k with some integrability conditions, the abovementioned problem has a unique sol
The Fredholm Alternative at the First Eigenvalue for the One Dimensionalp-Laplacian
✍ Scribed by Manuel del Pino; Pavel Drábek; Raul Manásevich
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 218 KB
- Volume
- 151
- Category
- Article
- ISSN
- 0022-0396
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
In this paper we characterize the set of all right-hand sides h ∈ C for which the boundary value problem . Here 1 < p < 2, and λ 1 > 0 is the first eigenvalue of the p-Laplacian. In particular, we prove that for hϕ 1 = 0 this problem is solvable and the energy functional is unbounded from below.
We investigate the existence and multiplicity of weak solutions u 2 W 1;p 0 ðOÞ to the degenerate quasilinear Dirichlet boundary value problem where z 2 R is a parameter. It is assumed that 1opo1; p=2; and O is a bounded domain in R N : The number l 1 stands for the first (smallest) eigenvalue of t
We studied the two known works on stability for isoperimetric inequalities of the first eigenvalue of the Laplacian. The earliest work is due to A. Melas who proved the stability of the Faber-Krahn inequality: for a convex domain contained in n with λ close to λ, the first eigenvalue of the ball B o
We prove here bifurcation and existence results for a nonlinear elliptic system involving the p -Laplacian. We say that i is an eigenvalue of (E,) if there exists a nontrivial pair (u,v) E ( W i ' p ) 2 1991 Mathematics Subject Classification. 35; 35 G ; 35 J. Keywords and phrases. p -Laplacian, sy
Let H be the upper half plane and X=SL(2, Z)"H the corresponding modular surface. Theory and experiment suggest that the eigenvalues of the hyperbolic Laplacian, 2, on X, denoted by \* j =1Â4+t 2 j , behave in many ways like a random sequence. In particular, for any A>0 the numbers A\* j , j=1, 2, 3