Existence of two nontrivial solutions for semilinear elliptic problems.
Existence of two positive solutions for a class of semilinear elliptic equations with singularity and critical exponent
We study the following singular elliptic equation with critical exponent ⎧ in Ω, ⎨u > 0 in Ω, ⎩u = 0 on ∂Ω, where (N≥3) is a smooth bounded domain, and λ > 0, γ ∈ (0,1) are real parameters. Under appropriate assumptions on Q, by the constrained minimizer and perturbation methods, we obtain two positive solutions for all λ > 0 small enough.
Existence of unstable sets for invariant sets in compact semiflows. Applications in order-preserving semiflows
Existence of Waves for a Nonlocal Reaction-Diffusion Equation
In this work we study a nonlocal reaction-diffusion equation arising in population dynamics. The integral term in the nonlinearity describes nonlocal stimulation of reproduction. We prove existence of travelling wave solutions by the Leray-Schauder method using topological degree for Fredholm and proper operators and special a priori estimates of solutions in weighted Hölder spaces.
Existence of weak solutions for a non-classical sharp interface model for a two-phase flow of viscous, incompressible fluids
Existence of weak solutions for a nonhomogeneous solidification mathematical model.
Existence of weak solutions for a nonlinear elliptic system.
Existence of weak solutions for a nonuniformly elliptic nonlinear system in .
Existence of weak solutions for a scale similarity model of the motion of large eddies in turbulent flow.
Existence of weak solutions for abstract hyperbolic-parabolic equations.
Existence of weak solutions for degenerate semilinear elliptic equations in unbounded domains.
Existence of weak solutions for elliptic Dirichlet problems with variable exponent
This paper presents several sufficient conditions for the existence of weak solutions to general nonlinear elliptic problems of the type where is a bounded domain of , . In particular, we do not require strict monotonicity of the principal part , while the approach is based on the variational method and results of the variable exponent function spaces.
Existence of weak solutions for mixed problems of parabolic systems.
Existence of weak solutions for nonlinear elliptic systems on .
Existence of weak solutions for nonlinear systems involving several -Laplacian operators.
Existence of weak solutions for quasilinear elliptic equations involving the -Laplacian.
Existence of weak solutions for steady flows of electrorheological fluid with Navier-slip type boundary conditions
We prove the existence of weak solutions for steady flows of electrorheological fluids with homogeneous Navier-slip type boundary conditions provided . To prove this, we show Poincaré- and Korn-type inequalities, and then construct Lipschitz truncation functions preserving the zero normal component in variable exponent Sobolev spaces.
Existence of weak solutions for the thermistor problem with degeneracy.
Existence of weak solutions to a class of degenerate semiconductor equations modeling avalanche generation.
Existence of weak solutions to doubly degenerate diffusion equations
We prove existence of weak solutions to doubly degenerate diffusion equations by Faedo-Galerkin approximation for general domains and general nonlinearities. More precisely, we discuss the equation in an abstract setting, which allows to choose function spaces corresponding to bounded or unbounded domains with Dirichlet or Neumann boundary conditions. The function can be an inhomogeneity or a nonlinearity involving terms of the form or . In the appendix, an introduction to weak differentiability...