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We prove interior gradient estimates for a large class of parabolic equations in divergence form. Using some simple ideas, we prove these estimates for several types of equations that are not amenable to previ...
We consider the following eigenvalue problems:
in
in
This paper deals with boundary value problems for second-order differential equations with deviating arguments. Some sufficient conditions are formulated under which such problems have quasisolutions or a uniq...
Let
be a divergence form operator with Lipschitz continuous coefficients in a domain
...
-Differential Forms and Quasiregular Mappings
A theorem on removable singularities of
-differential forms is proved and applied to quasiregular mappings.
We establish the global Hölder estimates for solutions to second-order elliptic equations, which vanish on the boundary, while the right-hand side is allowed to be unbounded. For nondivergence elliptic equatio...
We investigate the Dirichlet problem for the parabolic equation
in a nonsmooth and closed domain
We study overdetermined boundary conditions for positive solutions to some elliptic partial differential equations of
-Laplacian type in ...
We investigate local and global properties of positive solutions to the fast diffusion equation
in the good exponent range
We deal with the existence of positive solutions to impulsive second-order differential equations subject to some boundary conditions on the semi-infinity interval.
-Laplacian equations
By a variant version of mountain pass theorem, the existence and multiplicity of solutions are obtained for a class of superlinear
-Lapla...
A singular boundary value problem (BVP) for a second-order nonlinear differential equation is studied. This BVP is a model in hydrodynamics as well as in nonlinear field theory and especially in the study of t...
We show that every weak supersolution of a variable exponent
-Laplace equation is lower semicontinuous and that the singular set of such ...
We obtain some uniqueness results for the Dirichlet problem for second-order elliptic equations in an unbounded open set
without the cone proper...
The second-order nonlinear elliptic system
,
with
...
We study the existence of periodic solutions for second-order nonautonomous dynamical systems. We give four sets of hypotheses which guarantee the existence of solutions. We were able to weaken the hypotheses ...
A transmission problem involving two Euler-Bernoulli equations modeling the vibrations of a composite beam is studied. Assuming that the beam is clamped at one extremity, and resting on an elastic bearing at t...
We deal with the blowup properties of the solution to the degenerate and singular parabolic system with nonlocal source and homogeneous Dirichlet boundary conditions. The existence of a unique classical nonneg...
We investigate the questions of existence of positive solution for the nonlocal problem
and
Via the linking theorem, the existence of nontrivial solutions for a nonlinear elliptic Dirichlet boundary value problem with an inverse square potential is proved.
For a class of nonlinear elliptic boundary value problems in divergence form, we construct some general elliptic inequalities for appropriate combinations of
...
We consider the boundary value problem for the nonlinear Poisson equation with a nonlocal term
,
...
Uniqueness implies uniqueness relationships are examined among solutions of the fourth-order ordinary differential equation,
, satisfying
We address the pricing of American straddle options. We use a technique due to Kim (1990) to derive an expression involving integrals for the price of such an option close to expiry. We then evaluate this expr...
data
We prove an existence result for solutions of nonlinear parabolic inequalities with
data in Orlicz spaces.
The paper deals with the existence and nonexistence of positive solutions for a class of
-Laplacian systems. We investigate the effect of the siz...
A homogeneous boundary condition is constructed for the parabolic equation
in an arbitrary cylindrical domain
...
By Karamata regular variation theory, we show the existence and exact asymptotic behaviour of the unique classical solution
near the boundary to...
The method of generalized quasilinearization for second-order boundary value problems has been extended when the forcing function is the sum of
-...
We find a second-order approximation of the boundary blowup solution of the equation
, with
-Laplacian semipositone equations
We study positive
solutions to classes of boundary value problems of the form
We study the boundary regularity of weak solutions to nonlinear obstacle problem with
-obstacle function, and obtain the
...
A boundary-value problem for a semilinear elliptic equation in a convex ring is considered. Under suitable structural conditions, any classical solution
When solving boundary value problems on infinite intervals, it is possible to use continuation principles. Some of these principles take advantage of equipping the considered function spaces with topologies of...
We study a final value problem for first-order abstract differential equation with positive self-adjoint unbounded operator coefficient. This problem is ill-posed. Perturbing the final condition, we obtain an ...
The goal of this paper is to study the existence and the multiplicity of non-trivial weak solutions for some degenerate nonlinear elliptic equations on the whole space
...
For strongly singular higher-order linear differential equations together with two-point conjugate and right-focal boundary conditions, we provide easily verifiable best possible conditions which guarantee the...
We consider the problem
,
, where
...
Unimprovable efficient sufficient conditions are established for the unique solvability of the periodic problem
for
...
We investigate the existence of multiple solutions to quasilinear elliptic problems containing Laplace like operators (
-Laplacians). We are inte...
We study the uniqueness of positive solutions of the boundary value problem
,
We treat an initial boundary value problem for a nonlinear wave equation
in the domain
-Laplacian semipositone problem
We consider the boundary value problem
in
satisfying
...
For wave equations with power nonlinearity we investigate the problem of the existence or nonexistence of global solutions of the Cauchy characteristic problem in the light cone of the future.
-Laplacian problems by variational methods
We obtain multiple positive solutions of singular
-Laplacian problems using variational methods. The techniques are applicable to other types of ...
-Laplacian systems with nonlinear boundary conditions
We study the properties of the positive principal eigenvalue and the corresponding eigenspaces of two quasilinear elliptic systems under nonlinear boundary conditions. We prove that this eigenvalue is simple, ...
We study the existence of a class of nonlinear elliptic equation with Neumann boundary condition, and obtain infinitely many nodal solutions. The study of such a problem is based on the variational methods and...
The regularized system of equations for one model of a viscoelastic medium with memory along trajectories of the field of velocities is under consideration. The case of a changing domain is studied. We investi...
We develop monotone iterative technique for a system of semilinear elliptic boundary value problems when the forcing function is the sum of Caratheodory functions which are nondecreasing and nonincreasing, res...
We prove some existence theorems regarding solutions to boundary value problems for systems of second-order discrete inclusions. For a certain class of right-hand sides, we present some lemmas showing that all...
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