400 research outputs found
Existence results for quasilinear parabolic hemivariational inequalities
AbstractThis paper is devoted to the periodic problem for quasilinear parabolic hemivariational inequalities at resonance as well as at nonresonance. By use of the theory of multi-valued pseudomonotone operators, the notion of generalized gradient of Clarke and the property of the first eigenfunction, we build a Landesman–Lazer theory in the nonsmooth framework of quasilinear parabolic hemivariational inequalities
A class of BVPs for nonlinear fractional differential equations with p-Laplacian operator
In this paper, we study a class of integral boundary value problems of nonlinear differential equations of fractional order with p-Laplacian operator. Under some suitable assumptions, a new result on the existence of solutions is obtained by using a standard fixed point theorem. An example is included to show the applicability of our result
The solvability and optimal controls for some fractional impulsive equation
This paper is concerned with the existence and uniqueness of mild solution of some fractional impulsive equations. Firstly, we introduce the fractional calculus, Gronwall inequality, and Leray-Schauder’s fixed point theorem. Secondly with the help of them, the sufficient condition for the existence and uniqueness of solutions is presented. Finally we give an example to illustrate our main results
Multiple positive solutions for singular anisotropic Dirichlet problems
We consider a nonlinear Dirichlet problem driven by the variable exponent (anisotropic) p-Laplacian and a reaction that has the competing effects of a singular term and of a superlinear perturbation. There is no parameter in the equation (nonparametric problem). Using variational tools together with truncation and comparison techniques, we show that the problem has at least two positive smooth solutions
Dirichlet problems with unbalanced growth and convection
We consider a double phase Dirichlet problem with a gradient dependent reaction term (convection). Using the theory of nonlinear operators of monotone type, we show the existence of a bounded strictly positive solution. Moreover, we show that the set of these solutions is compact in the corresponding generalized Sobolev–Orlicz space
Singular anisotropic equations with a sign-changing perturbation
We consider an anisotropic Dirichlet problem driven by the variable (p, q)-Laplacian (double phase problem). In the reaction, we have the competing effects of a singular term and of a superlinear perturbation. Contrary to most of the previous papers, we assume that the perturbation changes sign. We prove a multiplicity result producing two positive smooth solutions when the coefficient function in the singular term is small in the L∞-norm
A double phase equation with convection
We consider a double phase problem with a gradient dependent reaction (convection). Using the theory of nonlinear operators of monotone type, we show the existence of a nontrivial, positive, bounded solution
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