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)

Elliptic variational problems with indefinite nonlinearities

NO ABSTRAC

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