In this article, we study the existence of solutions to systems of conformable fractional differential equations with periodic boundary value or initial value conditions. where the right member of the system is $L_{\alpha }^1$-carathéodory function. We employ the method of solution-tube and Schauder’s fixed-point theorem.

The purpose of the present paper is to study the existence of solutions to initial value problems for nonlinear first order differential systems subject to nonlinear nonlocal initial conditions of functional type. The approach uses vector-valued metrics and matrices convergent to zero. Two existence results are given by means of Schauder and Leray-Schauder fixed point principles and the existence and uniqueness of the solution is obtained via a fixed point theorem due to Perov. Two examples are...

In this paper, we study ϕ-Laplacian problems for differential inclusions with Dirichlet boundary conditions. We prove the existence of solutions under both convexity and nonconvexity conditions on the multi-valued right-hand side. The nonlinearity satisfies either a Nagumo-type growth condition or an integrably boundedness one. The proofs rely on the Bonhnenblust-Karlin fixed point theorem and the Bressan-Colombo selection theorem respectively. Two applications to a problem from control theory are...

In this paper we consider the existence, multiplicity, and nonexistence of positive solutions to fractional differential equation with integral boundary conditions. Our analysis relies on the fixed point index.

This paper treats the question of the existence of solutions of a fourth order boundary value problem having the following form: $x^{\left(4\right)}\left(t\right)+f(t,x\left(t\right),x^{\text{'}\text{'}}\left(t\right))=0$, 0 < t < 1, x(0) = x’(0) = 0, x”(1) = 0, $x^{\left(3\right)}\left(1\right)=0$. Boundary value problems of very similar type are also considered. It is assumed that f is a function from the space C([0,1]×ℝ²,ℝ). The main tool used in the proof is the Leray-Schauder nonlinear alternative.

We develop the existence theory for sequential fractional differential equations involving Liouville-Caputo fractional derivative equipped with anti-periodic type (non-separated) and nonlocal integral boundary conditions. Several existence criteria depending on the nonlinearity involved in the problems are presented by means of a variety of tools of the fixed point theory. The applicability of the results is shown with the aid of examples. Our results are not only new in the given configuration...

The existence of single and multiple nonnegative solutions for singular positone boundary value problems to the delay one-dimensional p-Laplacian is discussed. Throughout our nonlinearity f(·,y) may be singular at y = 0.

In this paper we establish the existence of single and multiple solutions to the positone discrete Dirichlet boundary value problem $$\left\{\begin{array}{c}\Delta \left[\phi \right(\Delta u(t-1)\left)\right]+q\left(t\right)f(t,u(t\left)\right)=0,t\in \{1,2,\cdots ,T\}\hfill \\ u\left(0\right)=u(T+1)=0,\hfill \end{array}\right.$$ where $\phi \left(s\right)={\left|s\right|}^{p-2}s$, $p>1$ and our nonlinear term $f(t,u)$ may be singular at $u=0$.

This paper studies the existence of solutions to the singular boundary value problem $$\left\}\begin{array}{c}-u^{\text{'}\text{'}}=g(t,u)+h(t,u),t\in (0,1),u\left(0\right)=0=u\left(1\right),\hfill \end{array}\right.$$ where $g(0,1)\times (0,\infty )\to ℝ$ and $h(0,1)\times [0,\infty )\to [0,\infty )$ are continuous. So our nonlinearity may be singular at $t=0,1$ and $u=0$ and, moreover, may change sign. The approach is based on an approximation method together with the theory of upper and lower solutions.

Dorsey, Di Bartolo and Dolgert (Di Bartolo et al., 1996; 1997) have constructed asymptotic matched solutions at order two for the half-space Ginzburg-Landau model, in the weak-$\kappa$ limit. These authors deduced a formal expansion for the superheating field in powers of ${\kappa }^{\frac{1}{2}}$ up to order four, extending the formula by De Gennes (De Gennes, 1966) and the two terms in Parr’s formula (Parr, 1976). In this paper, we construct asymptotic matched solutions at all orders leading to a complete expansion in powers...

Dorsey, Di Bartolo and Dolgert (Di Bartolo et al., 1996; 1997) have constructed asymptotic matched solutions at order two for the half-space Ginzburg-Landau model, in the weak-κ limit. These authors deduced a formal expansion for the superheating field in powers of ${\kappa }^{\frac{1}{2}}$ up to order four, extending the formula by De Gennes (De Gennes, 1966) and the two terms in Parr's formula (Parr, 1976). In this paper, we construct asymptotic matched solutions at all orders leading to a complete expansion...