On a holomorphic solution of a singular partial differential equation with many simple poles
We consider problem (P) of Kirchhoff-Carrier type with nonlinear terms containing a finite number of unknown values with By applying the linearization method together with the Faedo-Galerkin method and the weak compact method, we first prove the existence and uniqueness of a local weak solution of problem (P). Next, we consider a specific case of (P) in which the nonlinear term contains the sum . Under suitable conditions, we prove that the solution of converges to the solution of the corresponding...
Our aim in this paper is to study the existence of solutions to a phase-field system based on the Maxwell-Cattaneo heat conduction law, with a logarithmic nonlinearity. In particular, we prove, in one and two space dimensions, the existence of a solution which is separated from the singularities of the nonlinear term.
We prove existence/nonexistence and uniqueness of positive entire solutions for some semilinear elliptic equations on the Hyperbolic space.
We prove an existence theorem of Cauchy-Kovalevskaya type for the equation where f is a polynomial with respect to the last k variables.
We obtain new variants of weighted Gagliardo-Nirenberg interpolation inequalities in Orlicz spaces, as a consequence of weighted Hardy-type inequalities. The weights we consider need not be doubling.
We consider the problem of minimizing the energyamong all functions for which two level sets have prescribed Lebesgue measure . Subject to this volume constraint the existence of minimizers for is proved and the asymptotic behaviour of the solutions is investigated.
We consider the problem of minimizing the energy among all functions u ∈ SBV²(Ω) for which two level sets have prescribed Lebesgue measure . Subject to this volume constraint the existence of minimizers for E(.) is proved and the asymptotic behaviour of the solutions is investigated.