Existence of entropy solutions for a reacting Euler system.
Existence of least energy solutions to coupled elliptic systems with critical nonlinearities.
Existence of Local Smooth Solution for a Generalized Zakharov System.
Existence of local solutions for free boundary problems for viscous compressible barotropic fluids
We prove the local existence of solutions for equations of motion of a viscous compressible barotropic fluid in a domain bounded by a free surface. The solutions are shown to exist in exactly those function spaces where global solutions were found in our previous papers [14, 15].
Existence of many positive nonradial solutions for a superlinear Dirichlet problem on thin annuli.
Existence of Metrics With Prescribed Ricci Curvature: Local Theory.
Existence of mild solutions to semilinear evolution inclusions with nonlocal conditions.
Existence of minimizers for Kohn-Sham models in quantum chemistry
Existence of multiple principal eigenvalues for some indefinite linear eigenvalue problems
We study the existence of principal eigenvalues for differential operators of second order which are not necessarily in divergence form. We obtain results concerning multiplicity of principal eigenvalues in both the variational and the general case. Our approach uses systematically the Krein-Rutman theorem and fixed point arguments for the spectral radius of some associated problems. We also use a variational characterization for both the self-adjoint and the general case.
Existence of multiple solutions for a nonlinearly perturbed elliptic parabolic system in .
Existence of multiple solutions for a -Laplace equation.
Existence of multiple solutions for quasilinear diagonal elliptic systems.
Existence of non-negative solutions for a Dirichlet problem.
Existence of non-negative solutions for nonlinear equations in the semi-positone case.
Existence of nonnegative solutions to positone-type problems in with indefinite weights.
Existence of nontrivial solution for a nonlocal elliptic equation with nonlinear boundary condition.
Existence of nontrivial solutions for semilinear problems with strictly differentiable nonlinearity.
Existence of nontrivial solutions for singular quasilinear equations with sign changing nonlinearity.
Existence of optimal controls for control systems governed by nonlinear partial differential equations
Existence of optimal maps in the reflector-type problems
In this paper, we consider probability measures μ and ν on a d-dimensional sphere in and cost functions of the form that generalize those arising in geometric optics where We prove that if μ and ν vanish on -rectifiable sets, if |l'(t)|>0, and is monotone then there exists a unique optimal map To that transports μ onto where optimality is measured against c. Furthermore, Our approach is based on direct variational arguments. In the special case when existence of optimal maps...