Semilinear Elliptic Equations on Unbounded Domains.
Semilinear elliptic equations with measure data and quasi-regular Dirichlet forms
We are mainly concerned with equations of the form -Lu = f(x,u) + μ, where L is an operator associated with a quasi-regular possibly nonsymmetric Dirichlet form, f satisfies the monotonicity condition and mild integrability conditions, and μ is a bounded smooth measure. We prove general results on existence, uniqueness and regularity of probabilistic solutions, which are expressed in terms of solutions to backward stochastic differential equations. Applications include equations with nonsymmetric...
Semilinear elliptic problems in unbounded domains
We investigate the existence of positive solutions and their continuous dependence on functional parameters for a semilinear Dirichlet problem. We discuss the case when the domain is unbounded and the nonlinearity is smooth and convex on a certain interval only.
Semilinear elliptic problems on unbounded subsets of the Heisenberg group.
Semilinear elliptic problems with nonlinearities depending on the derivative
We deal with the boundary value problem where is an smooth bounded domain, is the first eigenvalue of the Laplace operator with homogeneous Dirichlet boundary conditions on , and is bounded and continuous. Bifurcation theory is used as the right framework to show the existence of solution provided that satisfies certain conditions on the origin and at infinity.
Semilinear equations, the function, and generalized Gauduchon metrics
In this paper, we generalize the Gauduchon metrics on a compact complex manifold and define the functions on the space of its hermitian metrics.
Semilinear equations with exponential nonlinearity and measure data
Semilinear geometric optics for generalized solutions.
Semilinear hyperbolic functional equations
We consider second order semilinear hyperbolic functional differential equations where the lower order terms contain functional dependence on the unknown function. Existence and uniqueness of solutions for t ∈ (0,T), existence for t ∈ (0,∞) and some qualitative properties of the solutions in (0,∞) are shown.
Semilinear Hyperbolic Systems and Equations with Singular Initial Data.
Semilinear hyperbolic systems in one space dimension with strongly singular initial data.
Semilinear integro-differential equations with compact semigroups.
Semilinear parabolic problems on manifolds and applications to the non-compact Yamabe problem.
Semilinear parabolic systems
Semilinear Poisson problems in Sobolev-Besov spaces on Lipschitz domains.
Extending recent work for the linear Poisson problem for the Laplacian in the framework of Sobolev-Besov spaces on Lipschitz domains by Jerison and Kenig [16], Fabes, Mendez and Mitrea [9], and Mitrea and Taylor [30], here we take up the task of developing a similar sharp theory for semilinear problems of the type Δu - N(x,u) = F(x), equipped with Dirichlet and Neumann boundary conditions.
Semilinear problems perturbed through the boundary condition
Semilinear problems with bounded nonlinear term.
Semilinear wave equation on manifolds
Semilinear wave equations with angularly smooth data
Semilinear waves with cusp singularities