Existence results for a mixed boundary value problem

In the present paper, we obtain an existence result for a class of mixed boundary value problems for second-order differential equations. A critical point theorem is used, in order to prove the existence of a precise open interval of positive eigenvalues $\lambda$, for which the considered problem admits at least one non-trivial classical solution $u_\lambda$. It is proved that the norm of $u_\lambda$ tends to zero as $\lambda \rightarrow 0$

Infinitely many solutions for a Dirichlet boundary value problem depending on two parameters

In this paper, using Ricceri\u27s variational principle, we prove the existence of infinitely many weak solutions for a Dirichlet doubly eigenvalue boundary value problem

Nontrivial solutions for nonlinear algebraic systems via a local minimum theorem for functionals

In this article, we use a critical point theorem (local minimum result) for differentiable functionals to prove the existence of at least one nontrivial solution for a nonlinear algebraic system with a parameter. Our goal is achieved by requiring an appropriate asymptotic behavior of the nonlinear term at zero. Some applications to discrete equations are also presented

Variational approach to fractional boundary value problems with two control parameters

This article concerns the multiplicity of solutions for a fractional differential equation with Dirichlet boundary conditions and two control parameters. Using variational methods and three critical point theorems, we give some new criteria to guarantee that the fractional problem has at least three solutions

Infinitely many solutions for p-Laplacian boundary-value problems on the real line

Under appropriate oscillating behaviour of the nonlinear term, we prove the existence of multiple solutions for p-Laplacian parametric equations on unbounded intervals. These problems have a variational structure, so we use an abstract result for smooth functionals defined on reflexive Banach spaces

Existence and multiplicity of solutions for a discrete nonlinear boundary value problem

In this article, we show the existence and multiplicity of positive solutions for a discrete nonlinear boundary value problem involving the p-Laplacian. Our approach is based on critical point theorems in finite dimensional Banach spaces

Steklov problems involving the p(x)-Laplacian

Under suitable assumptions on the potential of the nonlinearity, we study the existence and multiplicity of solutions for a Steklov problem involving the p(x)-Laplacian. Our approach is based on variational methods

Existence of solutions to Dirichlet impulsive differential equations through a local minimization principle

A critical point theorem (local minimum result) for differentiable functionals is used for proving that a Dirichlet impulsive differential equation admits at least one non-trivial solution. Some particular cases and a concrete example are also presented