相关论文: A mixed local-nonlocal H\'enon problem in $\mathbb…
In this paper, we establish some Harnack type inequalities satisfied by positive solutions of nonlocal inhomogeneous equations arising in the description of various phenomena ranging from population dynamics to micro-magnetism. For regular…
In this article, we prove an existence of solutions for a non-local boundary value problem with nonlinearity in a nonlocal condition. Our method is based upon the Mawhin's coincidence theory.
We prove the existence of a weak solution for boundary value problems driven by a mixed local--nonlocal operator. The main novelty is that such an operator is allowed to be nonpositive definite.
Here a mixed problem for a nonlinear hyperbolic equation with Neumann boundary value condition is investigated, and a priori estimations for the possible solutions of the considered problem are obtained. These results demonstrate that any…
We investigate existence and uniqueness of solutions for a class of nonlinear nonlocal problems involving the fractional $p$-Laplacian operator and singular nonlinearities.
In this paper we consider the problem $$ {ll} -\Delta u=(N+\a)(N-2)|x|^{\a}u^\frac{N+2+2\a}{N-2} & in R^N u>0& in R^N u\in D^{1,2}(R^N). $$ where $N\ge3$. From the characterization of the solutions of the linearized operator, we deduce the…
Given a bounded open set $\Omega\subseteq{\mathbb{R}}^n$, we consider the eigenvalue problem of a nonlinear mixed local/nonlocal operator with vanishing conditions in the complement of $\Omega$. We prove that the second eigenvalue…
We consider a class of nonlinear integro-differential equations whose leading operator is obtained as a superposition of $(-\Delta_{p})^{s}$ and $(-\Delta_{p})^{t}$, where $0<s<t<1<p<\infty$, weighted via two possibly degenerate…
In this article we consider a large family of nonlinear nonlocal equations involving gradient nonlinearity and provide a unified approach, based on the Ishii-Lions type technique, to establish Liouville properties of the solutions. We also…
In this paper, we study the regularity of solutions to a linear elliptic equation involving a mixed local-nonlocal operator of the form $$Lu - \operatorname{div}\big(a(x)\nabla u(x)\big)= f, \quad \text{in } \Omega \subset \mathbb{R}^n,$$…
This paper is devoted to study the existence of a solution to Hilfer fractional differential equation with nonlocal boundary condition. We use the equivalent integral equation to study the considered Hilfer differential problem with…
In this article, we establish radial symmetry for positive weak solutions of a class of mixed local-nonlocal equations with possibly singular nonlinearity via the moving plane method. Furthermore, we provide a quantitative version of…
The initial-boundary value problem in a bounded domain with moving boundaries and nonhomogeneous boundary conditions for a higher order nonlinear Schr\"odinger (HNLS) equation is considered. Existence and uniqueness of global weak solutions…
We put forward a strategy to achieve synthetic nonlinearities where local and nonlocal contributions compete on similar footing, thus yielding intermediate tunable responses ranging from fully local to strongly nonlocal. The physical…
We deal with a wide class of nonlinear nonlocal equations led by integro-differential operators of order $(s,p)$, with summability exponent $p \in (1,\infty)$ and differentiability exponent $s\in (0,1)$, whose prototype is the fractional…
We establish existence results for a class of mixed anisotropic and nonlocal $p$-Laplace equation with singular nonlinearities. We consider both constant and variable singular exponents. Our argument is based on an approximation method. To…
The aim of this paper is to study a nonlocal problem with a mixed Dirichlet-Neumann exterior condition. We prove existence, nonexistence and multiplicity of positive energy solutions and describe the interaction between the concave-convex…
In this paper, we establish the Harnack inequality of nonnegative weak solutions to the doubly nonlinear mixed local and nonlocal parabolic equations. This result is obtained by combining a related comparison principle, a local boundedness…
In this paper we establish the existence and uniqueness of solutions for nonlinear evolution equations on Banach space with locally monotone operators, which is a generalization of the classical result by J.L. Lions for monotone operators.…
In this article, we study an elliptic problem of mixed order with both local and nonlocal aspects involving singular nonlinearity in combination with critical Hartree-type nonlinearity. Using variational methods together with the critical…