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Positive solutions to the singular initial-boundary value problems
are obtained by applying the Schauder fixed-point theorem, where
This paper is concerned with the study of the Dirichlet problem for a class of second-order linear elliptic equations in weighted Sobolev spaces on unbounded domains of
...
We obtain asymptotic formulas for eigenvalues and eigenfunctions of the operator generated by a system of ordinary differential equations with summable coefficients and the quasiperiodic boundary conditions. U...
This paper is concerned with nonhomogeneous multipoint boundary value problems of second-order differential equations with one-dimensional
The study in this paper is a numerical integration of second-order three-point boundary value problems under two imposed nonlocal boundary conditions at
-Laplacian Boundary Value Problems with Dependence on the First-Order Derivative
This paper deals with the existence and iteration of positive solutions for the following one-dimensional
-Laplacian boundary value prob...
The existence of at least three positive solutions for differential equation
We study the global existence and the global nonexistence of a non-Newtonian polytropic filtration system coupled via nonlinear boundary flux. We first establish a weak comparison principle, then discuss the l...
Perturbation Functional at Nonresonance
This paper deals with a boundary value problem for Duffing equation. The existence of unique solution for the problem is studied by using the minimax theorem due to Huang Wenhua. The existence and uniqueness r...
-Laplacian Problems in Exterior Domains
We find the second positive radial solution for the following
-Laplacian problem:
This paper is devoted to the study of a mixed problem for a nonlinear parabolic integro-differential equation which mainly arise from a one dimensional quasistatic contact problem. We prove the existence and u...
We obtain the existence of a nontrivial solution for a class of subcritical elliptic systems with indefinite weights in
. The proofs bas...
Solving an inverse Sturm-Liouville problem requires a mathematical process to determine unknown function in the Sturm-Liouville operator from given data in addition to the boundary values. In this paper, we id...
Using the theory of coincidence degree, we establish existence results of positive solutions for higher-order multi-point boundary value problems at resonance for ordinary differential equation
For higher-order functional differential equations and, particularly, for nonautonomous differential equations with deviated arguments, new sufficient conditions for the existence and uniqueness of a periodic ...
The solvability for a class of abstract two-point boundary value problems derived from optimal control is discussed. By homotopy technique existence and uniqueness results are established under some monotonic ...
We are concerned with the nonlinear fourth-order three-point boundary value problem
,
...
We show the existence of four
-periodic solutions of the nonlinear Hamiltonian system with some conditions. We prove this problem by inv...
By mixed monotone method, the existence and uniqueness are established for singular higher-order continuous and discrete boundary value problems. The theorems obtained are very general and complement previous ...
Using fixed point index theory, we obtain several sufficient conditions of existence of at least one positive solution for third-order
-p...
We establish the existence of multiple positive solutions for a singular nonlinear third-order periodic boundary value problem. We are mainly interested in the semipositone case. The proof relies on a nonlinea...
We study the problem of finding a Hermitian monogenic function with a given jump on a given hypersurface in
. Necessary and sufficient condition...
-Point Boundary Value Problems
We consider the nonlinear eigenvalue problems
,
,
Using variational methods, we prove the existence and nonexistence of positive solutions for a class of
-Laplacian systems with a paramet...
-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...
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