Related papers: Quasilinear problems without the Ambrosetti-Rabino…
We study function-valued solutions of a class of stochastic partial differential equations, involving operators with polynomially bounded coefficients. We consider semilinear equations under suitable parabolicity hypotheses. We provide…
In this article, we establish the existence of solutions to the fractional $p-$Kirchhoff type equations with a generalized Choquard nonlinearities without assuming the Ambrosetti-Rabinowitz condition.
In this Note, we review the main existing results, methods, and some key open problems on the controllability of nonlinear hyperbolic and parabolic equations. Especially, we describe our recent universal approach to solve the local…
The work considers a system of fractional order partial differential equations. The existence and uniqueness theorems for the classical solution of initial-boundary value problems are proved in two cases: 1) the right-hand side of the…
We study the existence and multiplicity of positive solutions for the following concave-critical problem driven by an operator of mixed order obtained by the sum of the classical $p$-Laplacian and of the fractional $p$-Laplacian,…
We emphasize intertwining relations as a universal tool in constructing one-dimensional quasi-exactly solvable operators and offer their possible generalization to the multidimensional case. Considered examples include all quasi-exactly…
Two opposite constant-sign solutions to a non-variational p-Laplacian system with Robin boundary conditions are obtained via sub-super-solution techniques. A third nontrivial one comes out by means of topological degree arguments.
We establish conditions for nonexistence of global solutions for a class of quasilinear parabolic problems with a potential on complete, non-compact Riemannian manifolds, including the Porous Medium Equation and the p-Laplacian with a…
We investigate the existence and multiplicity of solutions to the following $p(x)$-Laplacian problem in $\mathbb{R}^{N}$ via critical point theory \begin{equation*} \left\{ \begin{array}{l} -\bigtriangleup _{p(x)}u+V(x)\left\vert…
We investigate inverse boundary problems associated with a time-dependent semilinear hyperbolic equation, where both nonlinearity and sources (including initial displacement and initial velocity) are unknown. We establish in several generic…
We find a solution of a quasilinear elliptic equation with Dirichlet's boundary condition on a smooth bounded domain and involving an unbounded continuous nonlinearity with oscillatory behavior near the origin.
The paper concerns boundary value problems for general nonautonomous first order quasilinear hyperbolic systems in a strip. We construct small global classical solutions, assuming that the right hand sides are small. In the case that all…
In the paper a new sufficient condition for the Aubin property to a class of parameterized variational systems is derived. In these systems the constraints depend both on the parameter as well as on the decision variable itself and they…
We establish uniqueness results for quasilinear elliptic problems through the criterion recently provided in \cite{DFMST}. We apply it to generalized $p$-Laplacian subhomogeneous problems that may admit multiple nontrivial nonnegative…
In this article we study the existence of weak solution, existence of ground state solution using Nehari manifold and existence of infinitely many solutions using Fountain theorem and Dual fountain theorem for a class of doubly nonlocal…
We present a simple algebraic procedure that can be applied to solve a range of quantum eigenvalue problems without the need to know the solution of the Schr\"odinger equation. The procedure, presented with a pedagogical purpose, is based…
This paper deals with existence and multiplicity of positive solutions for a quasilinear problem with Neumann boundary conditions, set in a ball. The problem admits at least one constant non-zero solution and it involves a nonlinearity that…
We consider a quasi-linear parabolic equation with nonlinear dynamic boundary conditions occurring as a natural generalization of the semilinear reaction-diffusion equation with dynamic boundary conditions. The corresponding class of…
In this paper, we study the existence of multiple solutions to a Caffarelli-Kohn-Nirenberg type equation with asymptotically linear term at infinity. In this case, the well-known Ambrosetti-Rabinowtz type condition doesn't hold, hence it is…
In this paper, we study a class of nonlinear Choquard type equations involving a general nonlinearity. By using the method of penalization argument, we show that there exists a family of solutions having multiple concentration regions which…