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Let be a bounded open convex set of class . Let be a non linear operator satisfying the condition (A) (elliptic) with constants , , . We prove that a number is an eigenvalue for the operator if and only if the number is an eigen-value for the operator . If , the two systems and have the same solutions. In particular, also the eventual eigen-values of the operator should all be negative. Finally, we obtain a sufficient condition for the existence of solutions of the system...
For a second order elliptic equation with a nonlinear radiation-type boundary condition on the surface of a three-dimensional domain, we prove existence of generalized solutions without explicit conditions (like ) on the trace of solutions. In the boundary condition, we admit polynomial growth of any fixed degree in the unknown solution, and the heat exchange and emissivity coefficients may vary along the radiating surface. Our generalized solution is contained in a Sobolev space with an exponent...
We show, by variational methods, that there exists a set open and dense in such that if then the problem , with subcritical (or more general nonlinearities), admits infinitely many solutions.
The paper is concerned with the study of an elliptic boundary value problem with a nonlinear Newton boundary condition considered in a two-dimensional nonpolygonal domain with a curved boundary. The existence and uniqueness of the solution of the continuous problem is a consequence of the monotone operator theory. The main attention is paid to the effect of the basic finite element variational crimes: approximation of the curved boundary by a polygonal one and the evaluation of integrals by numerical...
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