Related papers: Bounded Solutions to nonlinear problems involving …
We prove conditions for existence of analytical solutions for boundary value problems with the Hilfer fractional derivative, generalizing the commonly used Riemann-Liouville and Caputo operators. The boundary values, referred to in this…
This paper surveys recent analytical and numerical research on linear problems for the integral fractional Laplacian, fractional obstacle problems, and fractional minimal graphs. The emphasis is on the interplay between regularity,…
In this paper, we consider the indefinite fractional elliptic problem. A corresponding Liouville-type theorem for the indefinite fractional elliptic equations is established. Furthermore, we obtain a priori bound for solutions in a bounded…
By means of a recent variational technique, we prove the existence of radially monotone solutions to a class of nonlinear problems involving the $p$-Laplace operator. No subcriticality condition (in the sense of Sobolev spaces) is required.
The aim of this paper is to provide the first application of Theorem 3 of [2] in a case where the dependence of the underlying equation from the real parameter is not of affine type.
In this paper, we consider a fractional p-Laplacian system with both concave-convex nonlinearities and sign-changing weight functions in bounded domains. With the help of the Nehari\ manifold, we prove that the system has at least two…
The fractional Laplacian operator, $-(-\triangle)^{\frac{\alpha}{2}}$, appears in a wide class of physical systems, including L\'evy flights and stochastic interfaces. In this paper, we provide a discretized version of this operator which…
We study the solvability of boundary-value problems for differential-operator equations of the second order in L p (0, 1; X), with 1 < p < +$\infty$, X being a UMD complex Banach space. The originality of this work lies in the fact that we…
We study a Dirichlet problem driven by the (degenerate or singular) fractional $p$-Laplacian and involving a $(p-1)$-superlinear reaction at infinity, not necessarily satisfying the Ambrosetti-Rabinowitz condition. Using critical point…
In this note, we study the existence and uniqueness of a positive solution to a doubly singular fractional problem with nonregular data. Besides, for some cases, we will show the existence and uniqueness of another notion of a solution,…
We analyze a nonlocal diffusion operator having as special cases the fractional Laplacian and fractional differential operators that arise in several applications. In our analysis, a nonlocal vector calculus is exploited to define a weak…
We establish existence and uniqueness results for nonlinear elliptic Dirichlet boundary value problems on n-dimensional time scale domains. Time scales provide a unified framework that encompasses continuous, discrete, and hybrid settings.…
We adapt boundary deformation techniques to solve a Neumann problem for the Helmholtz equation with rough electric potentials in bounded domains. In particular, we study the dependance of Neumann eigenvalues of the perturbed Laplacian with…
We study a nonlinear, nonlocal Dirichlet problem driven by the degenerate fractional p-Laplacian via a combination of topological methods (degree theory for operators of monotone type) and variational methods (critical point theory). We…
Robin problem for the Laplacian in a bounded planar domain with a smooth boundary and a large parameter in the boundary condition is considered. We prove a two-sided three-term asymptotic estimate for the negative eigenvalues. Furthermore,…
We establish the existence and multiplicity of positive solutions to the problems involving the fractional Laplacian: \begin{equation*} \left\{\begin{array}{lll} &(-\Delta)^{s}u=\lambda u^{p}+f(u),\,\,u>0 \quad &\mbox{in}\,\,\Omega,\\…
We study an eigenvalue problem for the infinity-Laplacian on bounded domains. We prove the existence of the principal eigenvalue and a corresponding positive eigenfunction. The work also contains existence results when the parameter, in the…
We study the most general class of linear boundary-value problems for systems of $r$-th order ordinary differential equations whose solutions range over the complex H\"older space $C^{n+r,\alpha}$, with $0\leq n\in\mathbb{Z}$ and…
We analyze the existence and multiplicity of positive solutions to a nonlocal elliptic problem involving the spectral fractional Laplace operator endowed with homogeneous mixed Dirichlet-Neumann boundary conditions and weighted critical…
This paper analyzes the structure of the set of nodal solutions of a class of one-dimensional superlinear indefinite boundary values problems with an indefinite weight functions in front of the spectral parameter. Quite astonishingly, the…