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This paper deals with the existence of solutions to the following system:−Δu+u=αα+βa(x)|v|β|u|α−2u inRN−Δv+v=βα+βa(x)|u|α|v|β−2v inRN. With the help of the Nehari manifold and the linking theorem, we prove the existence of at least two nontrivial solutions. One of them is positive. Our main tools are the concentration-compactness principle and the Ekeland’s variational principle.
The paper is devoted to analysis of an elliptic-algebraic system of
equations describing heat explosion in a two phase medium filling a star-shaped domain. Three types
of solutions are found: classical, critical and
multivalued. Regularity of solutions is studied as well as their
behavior depending on the size of the domain and on the coefficient of
heat exchange between the two phases. Critical conditions of existence of solutions are found for arbitrary positive source function.
In this paper we are interested in the existence and uniqueness of solutions for the Navier problem associated to the degenerate nonlinear elliptic equations
in the setting of the weighted Sobolev spaces.
The paper is dedicated to the existence of local solutions of strongly nonlinear equations in RN and the Orlicz spaces framework is used.
Currently displaying 121 –
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