On the elliptic equation
On the Elliptic Equation ...u + K(x)e2u = 0 and Conformal Metrics with Prescribed Gaussian Curvatures..
On the Equation of Surfaces of Prescribed Mean Curvature. Existence and Uniqueness without Boundary Conditions.
On the existence and smoothness of radially symmetric solutions of a BVP for a class of nonlinear, non-Lipschitz perturbations of the Laplace equation.
On the existence and the stability of solutions for higher-order semilinear Dirichlet problems
We investigate the existence and stability of solutions for higher-order two-point boundary value problems in case the differential operator is not necessarily positive definite, i.e. with superlinear nonlinearities. We write an abstract realization of the Dirichlet problem and provide abstract existence and stability results which are further applied to concrete problems.
On the existence of a generalized solution to a three-dimensional elliptic equation with radiation boundary condition
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...
On the existence of a positive solution for a semilinear elliptic equation in the upper half space.
On the existence of blowing-up solutions for a mean field equation
On the existence of bounded solutions of nonlinear elliptic systems.
On the existence of five nontrivial solutions for resonant problems with p-Laplacian
In this paper we study a nonlinear Dirichlet elliptic differential equation driven by the p-Laplacian and with a nonsmooth potential. The hypotheses on the nonsmooth potential allow resonance with respect to the principal eigenvalue λ₁ > 0 of . We prove the existence of five nontrivial smooth solutions, two positive, two negative and the fifth nodal.
On the existence of multiple positive entire solutions for a class of quasilinear elliptic equations.
On the existence of multiple positive solutions for a certain class of elliptic problems
We investigate the existence of solutions for the Dirichlet problem including the generalized balance of a membrane equation. We present a duality theory and variational principle for this problem. As one of the consequences of the duality we obtain some numerical results which give a measure of a duality gap between the primal and dual functional for approximate solutions.
On the existence of multiple solutions for a class of nonlinear boundary value problems
On the existence of nonnegative radial solutions for p-Laplacian elliptic systems
The existence of nonnegative radial solutions for some systems of m (m ≥ 1) quasilinear elliptic equations is proved by a simple application of a fixed point theorem in cones.
On the existence of nontrivial solutions for a fourth-order semilinear elliptic problem.
On the existence of solutions of boundary-value problems for elastic-inelastic solids
On the existence of solutions to a class of -Laplace elliptic equations.
On the existence of weak solutions for some quasilinear elliptic variational boundary value problems at resonance
On the existence of weak solutions of perturbated systems with critical growth.
On the Exterior Capillarity Problem.