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-Laplacian
The paper discusses the existence of positive solutions, dead core solutions, and pseudo dead core solutions of the singular problem
,
We study existence of positive solutions of the nonlinear system
in
In a recent paper, Sun et al. (2007) studied the existence of positive solutions of nonhomogeneous multipoint boundary value problems for a second-order differential equation. It is the purpose of this paper t...
This paper is concerned with an initial boundary value problem in one-dimensional magnetohydrodynamics. We prove the global existence, uniqueness, and stability of strong solutions for the planar magnetohydrod...
-Point Boundary Value Problems with Impulses
By Leray-Schauder continuation theorem and the nonlinear alternative of Leray-Schauder type, the existence of a solution for an
-point bo...
This work is concerned with the relaxation-time limit of the multidimensional isothermal Euler equations with relaxation. We show that Coulombel-Goudon's results (2007) can hold in the weaker and more general Sob...
Krasnoselskii's fixed-point theorem in a cone is used to discuss the existence of positive solutions to semipositone right focal eigenvalue problems
We construct for every fixed
the metric
, where
-Laplacian Operator
The existence of positive solutions for boundary value problems of nonlinear functional difference equations with
-Laplacian operator is investig...
We consider the existence of minimal and maximal solutions of periodic boundary value problems for first-order impulsive integrodifferential equations of mixed-type on time scales by establishing a comparison ...
-Laplacian
A monotone iterative technique is applied to prove the existence of the extremal positive pseudosymmetric solutions for a three-point second-order
This paper considers the properties of positive solutions for a nonlocal equation with nonlocal boundary condition
on
A generalization of the comparison principle for a semilinear and a quasilinear parabolic equations with nonlocal boundary conditions including changing sign kernels is obtained. This generalization uses a pos...
We prove a linear and a nonlinear generalization of the Lax-Milgram theorem. In particular, we give sufficient conditions for a real-valued function defined on the product of a reflexive Banach space and a nor...
We are concerned with the nonlinear second-order impulsive periodic boundary value problem
,
...
This paper deals with a semilinear parabolic system in a bounded interval, completely coupled at the boundary with exponential type. We characterize completely the range of parameters for which nonsimultaneous...
-Point Boundary Value Problem
We study the second-order
-point boundary value problem
,
th-Order Singular Nonlocal Boundary Value Problems
We study the existence and multiplicity of positive solutions for a class of
th-order singular nonlocal boundary value problems
Data
We establish Hölder continuity of generalized solutions of the Dirichlet problem, associated to a degenerate nonlinear fourth-order equation in an open bounded set
...
We study the existence of positive solutions for a class of degenerate nonlinear elliptic equations with gradient dependence. For this purpose, we combine a blowup argument, the strong maximum principle, and L...
We report on some Liouville-type theorems for a class of linear second-order partial differential equation with nonnegative characteristic form. The theorems we show improve our previous results.
-Homogeneous Forms with a Potential in the Kato Class
We define a notion of Kato class of measures relative to a Riemannian strongly local
-homogeneous Dirichlet form and we prove a Harnack i...
Some existence theorems of the positive solutions and the multiple positive solutions for singular and nonsingular systems of nonlinear fourth-order boundary value problems are proved by using topological degr...
The aim of this article is to give an introduction to certain inequalities named after Carl Gustav Axel von Harnack. These inequalities were originally defined for harmonic functions in the plane and much late...
We prove a boundary comparison principle for positive infinity-harmonic functions for smooth boundaries. As consequences, we obtain (a) a doubling property for certain positive infinity-harmonic functions in s...
We consider the problem
where
is not identically zero. Under...
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
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