On elliptic problems with a nonlinearity depending on the gradient

We investigate the solvability of the Neumann problem $(1.1)$ involving the nonlinearity depending on the gradient. We prove the existence of a solution when the right hand side $f$ of the equation belongs to $L^m(\Omega )$ with $1 \leq m \lt 2$

Multiple solutions for a nonlinear Neumann problem involving

We study the nonlinear Neumann problem (1) involving a critical Sobolev exponent and a nonlinearity of lower order. Our main results assert that for every k∈ℕ problem (1) admits at least k pairs of nontrivial solutions provided a parameter μ; belongs to some interval (0, μ*)

Sur un systeme non lineaire d'inegalites aux derivees partielles du type parabolique

"Rozważa się układ nierówności różniczkowych typu parabolicznego (w sensie J. Szarskiego) postaci (...)" (fragm. streszczenia

Asymptotic estimates for solutions of the second boundary value problem for parabolic equations

Let .Q be an unbounded domain in Rn . We denote the boundary of Q by dQ. We consider the second boundary value problem n n (1 ) | f - = ) U i j ^ ' ^ V x. + X L + c ^ t » x , u in (0, oo ) x Q , ( 2 ) diiigi = 0 f o r (t,x) 6 (0, oo)x ai? , (3) u(0,x) = f i x ) for x e Q , where ¿^(fr x j denotes the inward conormal derivative to ( 0 , < » ) x 3 i P a t the point ( t , x ) (Fragment tekstu)

The Hardy potential and eigenvalue problems

We establish the existence of principal eigenfunctions for the Laplace operator involving weighted Hardy potentials. We consider the Dirichlet and Neumann boundary conditions

On a singular nonlinear Neumann problem

We investigate the solvability of the Neumann problem involving two critical exponents: Sobolev and Hardy-Sobolev. We establish the existence of a solution in three cases: (i) 2 < p + 1 < 2*(s), (ii) p + 1 = 2*(s) and (iii) 2*(s) < p + 1 ≤ 2*, where 2*(s) = 2(N-s)/N-2, 0 < s < 2, and 2* = 2(N-s)/N-2 denote the critical Hardy-Sobolev exponent and the critical Sobolev exponent, respectively

Elliptic variational problems with indefinite nonlinearities

NO ABSTRAC

The Dirichlet problem with L2-boundary data for elliptic linear equations

The Dirichlet problem has a very long history in mathematics and its importance in partial differential equations, harmonic analysis, potential theory and the applied sciences is well-known. In the last decade the Dirichlet problem with L2-boundary data has attracted the attention of several mathematicians. The significant features of this recent research are the use of weighted Sobolev spaces, existence results for elliptic equations under very weak regularity assumptions on coefficients, energy estimates involving L2-norm of a boundary data and the construction of a space larger than the usual Sobolev space W1,2 such that every L2-function on the boundary of a given set is the trace of a suitable element of this space. The book gives a concise account of main aspects of these recent developments and is intended for researchers and graduate students. Some basic knowledge of Sobolev spaces and measure theory is required