Related papers: Controlling monotonicity of nonlinear operators
We show the various existence results for degenerate $p(x)$-Laplace equations with Leray-Lions type operators. A suitable condition on degeneracy is discussed and proofs are mainly based on direct methods and critical point theories in…
In this manuscript we study the well-posedness of the master equations for mean field games with volatility control. This infinite dimensional PDE is nonlinear with respect to both the first and second-order derivatives of its solution. For…
Quantitative stochastic homogenization of linear elliptic operators is by now well-understood. In this contribution we move forward to the nonlinear setting of monotone operators with $p$-growth. This work is dedicated to a quantitative…
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.…
We prove an existence result for a class of Dirichlet boundary value problems with discontinuous nonlinearity and involving a Leray-Lions operator. The proof combines monotonicity methods for elliptic problems, variational inequality…
We consider positive singular solutions (i.e. with a non-removable singularity) of a system of PDEs driven by $p$-Laplacian operators and with the additional presence of a nonlinear first order term. By a careful use of a rather new version…
In this article we discuss the solvability of some class of fully nonlinear equations, and equations with p-Laplacian in more general conditions by using a new approach given in [1] for studying the nonlinear continuous operator. Moreover…
In this paper we study second order non-linear periodic systems driven by the ordinary vector $p$-Laplacian with a non-smooth, locally Lipschitz potential function. Our approach is variational and it is based on the non-smooth critical…
In this paper we study evolution problems of Leray-Lions type with nonhomogeneous Neumann boundary conditions in the framework of metric random walk spaces. This covers cases with the $p$-Laplacian operator in weighted discrete graphs and…
In this paper we study nonlinear second-order differential inclusions involving the ordinary vector $p$-Laplacian, a multivalued maximal monotone operator and nonlinear multivalued boundary conditions. Our framework is general and unifying…
In this paper, we investigate the monotonicity of solutions for a nonlinear equations involving the fractional Laplacian with variable exponent. We first prove different maximum principles involving this operator. Then we employ the direct…
We discuss the existence and regularity of solutions to a quasi-linear elliptic equation involving a Leray-Lions operator and a convection term with superlinear growth. In particular, equations involving the p-Laplacian are covered. This…
In this work, we study the existence and multiplicity of solutions for a class of problems involving the $\phi$-Laplacian operator in a bounded domain, where the nonlinearity has a critical growth. The main tool used is the variational…
We show some examples for uniformly monotone operators arising in weak formulation of nonlinear elliptic and parabolic problems. Besides the classical $p$-Laplacian some other less known examples are given which might be of interest because…
We prove the existence of solution for a class of $p(x)$-Laplacian equations where the nonlinearity has a critical growth. Here, we consider two cases: the first case involves the situation where the variable exponents are periodic…
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.
We propose a method of obtaining a posteriori estimates which does not use the duality theory and which applies to variational inequalities with monotone operators, without assuming the potentiality of operators. The effectiveness of the…
In the present paper we obtain growth monotonicity estimates of the principal Dirichlet-Laplacian eigenvalue in bounded non-Lipschitz domains. The proposed method is based on composition operators generated by quasiconformal mappings and…
In this paper we extend the well-known concentration -- compactness principle of P.L. Lions to Orlicz spaces. As an application we show an existence result to some critical elliptic problem with nonstandard growth.
In this article we consider the nonlinear system involving the $p$-Laplacian $$\left\{\begin{array}{lc} |u^\prime |^{p-2} u^{\prime \prime} = u^{p-1} v^p& |v^\prime |^{p-2} v^{\prime \prime} = v^{p-1} u^p&\ {\rm on} \ \R, u\geq 0, v\geq 0&…