23 research outputs found
Existence of three solutions for quasilinear elliptic equations: an Orlicz-Sobolev space setting
In this paper,we establish the existence of three weak solutions for quasilinear elliptic equations in an Orlicz-Sobolev space via an abstract result recently obtained by Ricceri in [13].In this paper, we establish the existence of three weak solutions for quasilinear elliptic equations in an Orlicz-Sobolev space via an abstract result recently obtained by Ricceri in [13].National Natural Science Foundation of China [11626038
Least energy sign-changing solution for degenerate Kirchhoff double phase problems
In this paper we study the following nonlocal Dirichlet equation of double
phase type
\begin{align*}
-\psi \left [ \int_\Omega \left ( \frac{|\nabla u |^p}{p} + \mu(x)
\frac{|\nabla u|^q}{q}\right)\,\mathrm{d} x\right] \mathcal{G}(u) = f(x,u)\quad
\text{in } \Omega, \quad u = 0\quad \text{on } \partial\Omega,
\end{align*}
where is the double phase operator given by
\begin{align*}
\mathcal{G}(u)=\operatorname{div} \left(|\nabla u|^{p-2}\nabla u + \mu(x)
|\nabla u|^{q-2}\nabla u \right)\quad u\in W^{1,\mathcal{H}}_0(\Omega),
\end{align*}
, , is a bounded domain with Lipschitz
boundary , , , , for
, with , and , and
is a Carath\'{e}odory function
that grows superlinearly and subcritically. We prove the existence of two
constant sign solutions (one is positive, the other one negative) and of a
sign-changing solution which has exactly two nodal domains and which turns out
to be a least energy sign-changing solution of the problem above. Our proofs
are based on variational tools in combination with the quantitative deformation
lemma and the Poincar\'{e}-Miranda existence theorem
Multiple solutions for a perturbed mixed boundary value problem involving the one-dimensional -Laplacian
The existence of three distinct weak solutions for a perturbed mixed boundary value problem involving the one-dimensional -Laplacian operator is established under suitable assumptions on the nonlinear term. Our approach is based on recent variational methods for smooth functionals defined on reflexive Banach spaces
Infinitely many solutions for a Dirichlet boundary value problem depending on two parameters
In this paper, using Ricceri\u27s variational principle, we prove the existence of infinitely many weak solutions for a Dirichlet doubly eigenvalue boundary value problem
Multiplicity of solutions to non-local problems of Kirchhoff type involving Hardy potential
The aim of this paper is to establish the existence of a sequence of infinitely many small energy solutions to nonlocal problems of Kirchhoff type involving Hardy potential. To this end, we used the Dual Fountain Theorem as a key tool. In particular, we describe this multiplicity result on a class of the Kirchhoff coefficient and the nonlinear term which differ from previous related works. To the best of our belief, the present paper is the first attempt to obtain the multiplicity result for nonlocal problems of Kirchhoff type involving Hardy potential by utilizing the Dual Fountain Theorem
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Optimal Constants in the Theory of Sobolev Spaces and PDEs
Recent research activities on sharp constants and optimal inequalities have shown their impact on a deeper understanding of geometric, analytical and other phenomena in the context of partial differential equations and mathematical physics. These intrinsic questions have applications not only to a-priori estimates or spectral theory but also to numerics, economics, optimization, etc
Differentiable positive definite kernels on two-point homogeneous spaces
In this work we study continuous kernels on compact two-point homogeneous spaces which are positive definite and zonal (isotropic). Such kernels were characterized by R. Gangolli some forty years ago and are very useful for solving scattered data interpolation problems on the spaces. In the case the space is the d-dimensional unit sphere, J. Ziegel showed in 2013 that the radial part of a continuous positive definite and zonal kernel is continuously differentiable up to order â(dâ1)/2â in the interior of its domain. The main issue here is to obtain a similar result for all the other compact two-point homogeneous spaces.CNPq (grant 141908/2015-7)FAPESP (grant 2014/00277-5