Variational Approach to Impulsive Differential Equations with Dirichlet Boundary Conditions

Variational Approach to Impulsive Differential Equations with Dirichlet Boundary Conditions

We study the existence of n distinct pairs of nontrivial solutions for impulsive differential equations with Dirichlet boundary conditions by using variational methods and critical point theory.

Stochastic Partial Differential Equations with Dirichlet White-noise Boundary Conditions

– The paper is devoted to one-dimensional nonlinear stochastic partial differential equations of parabolic type with non homogeneous Dirichlet boundary conditions of white-noise type. We formulate a set of conditions that a random field must satisfy to solve the equation. We show that a unique solution exists and that we can write it in terms of the stochastic kernel related to the problem. Thi...

Variational approach to a class of impulsive differential equations

Variational Method to the Impulsive Equation with Neumann Boundary Conditions

We study the existence and multiplicity of classical solutions for second-order impulsive SturmLiouville equation with Neumann boundary conditions. By using the variational method and critical point theory, we give some new criteria to guarantee that the impulsive problem has at least one solution, two solutions, and infinitely many solutions under some different conditions, respectively. Some ...

Variational Methods to Mixed Boundary Value Problem for Impulsive Differential Equations with a Parameter

In this paper, we study mixed boundary value problem for secondorder impulsive differential equations with a parameter. By using critical point theory, several new existence results are obtained. This is one of the first times that impulsive boundary value problems are studied by means of variational methods.