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We establish the existence of weak solutions of a nonlinear radiation-type boundary value problem for elliptic equation on divergence form with discontinuous leading coefficient. Quantitative estimates play a crucial role on the real…
We prove existence of solution to a local fractional nonlinear differential equation with initial condition. For that we introduce the notion of tube solution.
We overview a series of recent works addressing numerical simulations of partial differential equations in the presence of some elements of randomness. The specific equations manipulated are linear elliptic, and arise in the context of…
We analyze solvability of a special form of distributed order fractional differential equations within the space of tempered distributions supported by the positive half-line.
In this work we establish existence and multiplicity of solutions for elliptic problem with nonlinear boundary conditions under strong resonance conditions at infinity. The nonlinearity is resonance at infinity and the reso- nance phenomena…
By topological arguments, we prove new results on the existence, non-existence, localization and multiplicity of nontrivial solutions of a class of perturbed nonlinear integral equations. These type of integral equations arise, for example,…
In this article, we consider a combination of local and nonlocal Laplace equation with singular nonlinearities. For such mixed problems, we establish existence of at least one weak solution for a parameter dependent singular nonlinearity…
This paper is devoted to study the existence and uniqueness of solutions of a one parameter family of nonlinear fractional differential equation with mixed boundary value conditions. Riemann-Liouville fractional derivative is considered. An…
Fractional-order elliptic problems are investigated in case of inhomogeneous Dirichlet boundary data. The boundary integral form is proposed as a suitable mathematical model. The corresponding theory is completed by sharpening the mapping…
In this paper we consider a singular wave equation with distributional and more singular non-distributional coefficients and develop tools and techniques for the phase-space analysis of such problems. In particular we provide a detailed…
In this paper, we used some theorems of fixed point for studying the results of Existence and Uniqueness For Hilfer-Hadamard-Type Fractional Differential Equations, \[_{H}D^{\alpha,\beta}x(t)+f(t,x(t))=0, ~~~~~~ on~~the~~ interval~~…
In this paper we consider quasilinear elliptic equations with double phase phenomena and a reaction term depending on the gradient. Under quite general assumptions on the convection term we prove the existence of a weak solution by applying…
We obtain fundamental imbeddings for the fractional Sobolev space with variable exponent that is a generalization of well-known fractional Sobolev spaces. As an application, we obtain a-priori bounds and multiplicity of solutions to some…
In this paper, we study the positive solutions to the following singular and non local elliptic problem posed in a bounded and smooth domain $\Omega\subset \R^N$, $N> 2s$: % \begin{eqnarray*} (P_\lambda)\left\{\begin{array}{lll}…
We study uniqueness of solutions to degenerate parabolic problems, posed in bounded domains, where no boundary conditions are imposed. Under suitable assumptions on the operator, uniqueness is obtained for solutions that satisfy an…
It is considered a semilinear elliptic partial differential equation in $\mathbb{R}^N$ with a potential that may vanish at infinity and a nonlinear term with subcritical growth. A positive solution is proved to exist depending on the…
Bounded variation estimates of Galerkin approximations are established in order to extract an almost everywhere convergent subsequence of Galerkin approximations. As a result we prove existence of weak solutions of initial boundary value…
Utilising the notion of measures of non-compactness and Kamke function of order $\alpha$, we address the question of solvability of fractional differential equations in Banach spaces. In particular, we provide sufficient conditions ensuring…
n this paper, we prove existence of nodal solutions for singular semilinear elliptic systems without variational structure where its both components are of sign changing. Our approach is based on sub-supersolutions method combined with…
For a class of non-autonomous parabolic stochastic partial differential equations defined on a bounded open subset $D\subset \mathbb {R}^d$ and driven by an $L^2(D)$-valued fractional Brownian motion with the Hurst index $H>1/2$, a new…