J. Chabrowski, P. M. Girão (2001)
Colloquium Mathematicae
Similarity:
We prove sharp inequalities in weighted Sobolev spaces. Our approach is based on the blow-up technique applied to some nonlinear Neumann problems.
Jan Chabrowski, Jianfu Yang (2005)
Annales Polonici Mathematici
Similarity:
We establish the existence of multiple solutions of an asymptotically linear Neumann problem. These solutions are obtained via the mountain-pass principle and a local minimization.
J. Chabrowski (2007)
Colloquium Mathematicae
Similarity:
We investigate the solvability of the linear Neumann problem (1.1) with L¹ data. The results are applied to obtain existence theorems for a semilinear Neumann problem.
Hichem Ben-El-Mechaiekh, Robert Dimand (2007)
Banach Center Publications
Similarity:
Liliana Klimczak (2015)
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
Similarity:
We consider a nonlinear Neumann problem with a nonhomogeneous elliptic differential operator. With some natural conditions for its structure and some general assumptions on the growth of the reaction term we prove that the problem has two nontrivial solutions of constant sign. In the proof we use variational methods with truncation and minimization techniques.
Christ, Michael (1998)
Documenta Mathematica
Similarity:
Jan Chabrowski, Kyril Tintarev (2005)
Bulletin of the Polish Academy of Sciences. Mathematics
Similarity:
We establish the existence of a solution to the Neumann problem in the half-space with a subcritical nonlinearity on the boundary. Solutions are obtained through the constrained minimization or minimax. The existence of solutions depends on the shape of a boundary coefficient.
Harold P. Boas, Emil J. Straube (1991)
Mathematische Zeitschrift
Similarity:
Jan Chabrowski, Bernhard Ruf (2007)
Colloquium Mathematicae
Similarity:
We investigate the solvability of the Neumann problem (1.1) involving a critical Sobolev exponent and lower order perturbations in bounded domains. Solutions are obtained by min max methods based on a topological linking. A nonlinear perturbation of a lower order is allowed to interfere with the spectrum of the operator -Δ with the Neumann boundary conditions.
Otto Moeschlin (2006)
Banach Center Publications
Similarity:
Anna Maria Candela, Monica Lazzo (1994)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
Similarity:
In this paper we study the influence of the domain topology on the multiplicity of solutions to a semilinear Neumann problem. In particular, we show that the number of positive solutions is stable under small perturbations of the domain.
J. Chabrowski, Jianfu Yang (2001)
Colloquium Mathematicae
Similarity:
We consider the Neumann problem for an elliptic system of two equations involving the critical Sobolev nonlinearity. Our main objective is to study the effect of the coefficient of the critical Sobolev nonlinearity on the existence and nonexistence of least energy solutions. As a by-product we obtain a new weighted Sobolev inequality.
H. Woźniakowski (1971)
Applicationes Mathematicae
Similarity:
Jan Chabrowski (2004)
Colloquium Mathematicae
Similarity:
We consider the Neumann problem involving the critical Sobolev exponent and a nonhomogeneous boundary condition. We establish the existence of two solutions. We use the method of sub- and supersolutions, a local minimization and the mountain-pass principle.
So-Chin Chen (1988)
Mathematische Zeitschrift
Similarity:
Joanna Rencławowicz, Wojciech M. Zajączkowski (2010)
Applicationes Mathematicae
Similarity:
We consider the Poisson equation with the Dirichlet and the Neumann boundary conditions in weighted Sobolev spaces. The weight is a positive power of the distance to a distinguished plane. We prove the existence of solutions in a suitably defined weighted space.